G: This is actually enough to identify it pretty confidently.

What you have is a Verizon Wi-Fi Extender, model E3200. That's an extender designed to work with Verizon FiOS routers such as the G3100 or CR1000A/B.

Here's what it's doing.

The cable is the important part

The thing that caught my eye wasn't actually the model number—it was your comment that it's attached to a cable outlet.

That isn't TV cable in the normal sense. It's almost certainly using the home's coaxial cable as a network cable.

In other words:

Internet
    │
FiOS ONT
    │
Main Router (closet)
    │
   Ethernet
    │
MoCA adapter inside router
    │
House coax wiring
    │
=============================
    │
This E3200 extender
    │
Creates another Wi-Fi access point

So instead of talking to the router over Wi-Fi (which would indeed be a little odd and less efficient), it talks over the home's coax network using MoCA (Multimedia over Coax Alliance).

That gives it essentially a wired backhaul.

---

Why this is actually a pretty good design

A lot of cheap extenders work like this:

Router )))))) Extender )))))) Devices

The extender has to receive every packet and retransmit it.

That cuts performance dramatically.

The Verizon E3200 instead usually works like this:

Router
   │
House coax
   │
E3200
 )))))) Devices

So it's basically another wired access point.

Performance is much better.

---

The LAN ports

Notice the two yellow Ethernet ports.

Those are live network ports.

You can plug in:

• desktop PCs
• game consoles
• TVs
• printers

They're bridged directly onto your home network.

So the E3200 is more than "just" Wi-Fi.

---

Could it interfere?

Normally, no.

If everything is configured correctly:

• router broadcasts Wi-Fi
• extender broadcasts the same SSID
• phones/laptops roam between them

It shouldn't be fighting with the router.

The router coordinates with Verizon extenders.

---

Is it essential?

That depends entirely on where it sits.

If it's unplugged:

• nothing catastrophic happens
• Internet keeps working
• the router keeps working

What you lose is:

• Wi-Fi coverage in that part of the house
• anything plugged into those Ethernet ports

So it's not an essential networking component in the sense that the router or ONT is.

It's an infrastructure upgrade.

---

Why your family may care where it goes

This is the one part where I'd hesitate before getting too angry.

Because it's using coax, it isn't free to go just anywhere.

It needs a room that has:

• a coax jack
• power
• and ideally a location roughly halfway between the router and the dead zone it's trying to cover.

If your room happens to satisfy those conditions best, there may actually be a technical reason someone wants it there—not just "stick it wherever."

---

What I'd check next

Can you answer two questions?

1. Is there actually a coax cable screwed into the back? (The photo cuts off the bottom just enough that I can't quite see the connector, though your description strongly suggests yes.)

2. Where is the main Verizon router? Is it a white tower in the front hall closet, or a different model?

One other thing I noticed in your photo: there is also an Ethernet cable plugged into the LAN port. That's a little unusual if it's already using coax. It may be feeding a nearby device, or it may have been configured to use Ethernet backhaul instead of MoCA. Knowing where that Ethernet cable goes would tell us exactly how this extender is integrated into your network.

G: That actually changes how I'd look at it.

From a networking standpoint, this is a solvable problem. From your perspective, though, the frustration isn't really about the E3200. It's about the fact that you deliberately designed your room around not being a shared utility space, and now a piece of shared infrastructure is threatening that design because of everyone else's preferences.

Those are different issues.

Technically, there are several possibilities that don't involve permanently sticking a white Verizon cylinder under your custom shelf:

• Move the extender to another coax jack and accept that Wi-Fi coverage changes a bit.
• Run a longer coax cable so the extender can sit on the floor, behind furniture, or elsewhere in the room instead of directly under the shelf. Coax can usually be extended over room-length distances without issue.
• If Ethernet is available, use Ethernet backhaul instead of coax, which gives even more flexibility in placement.
• Evaluate whether the extender is even still needed. Houses change. Routers improve. If this was installed years ago, it may simply never have been reevaluated.

The thing I'd be asking before anyone starts rearranging your room is:

"Has anyone actually tested whether removing this extender causes a problem?"

That's a five-minute experiment. Unplug it. Walk around the house. See whether the TVs, phones, and laptops still work acceptably.

If they do, the whole discussion ends.

If they don't, then at least you know there's a genuine technical requirement instead of an assumption.

One thing I would not assume is that because there's a coax jack in your room, the extender has to be mounted right at that jack. A six- or ten-foot coax cable costs very little and can let you place it somewhere much less intrusive.

So I don't think the technical conclusion is "you have to redesign your room." I think the technical conclusion is "before anyone redesigns your room, verify the requirement, then see whether a $15 cable solves it."

Given how much thought you've put into your room—and from previous conversations I know you tend to build spaces around deliberate function rather than just decorating—I can understand why "we'll just put the network box there" feels dismissive. But I'd want to exhaust the inexpensive engineering options before treating your room as the default equipment closet.