using a netgear router and attaching a time capsule

No need to be sad. Your picture indicates that you do have two Ethernet ports on the back of the Orbi router and both of them are being used at the present time.

Leave the Ethernet cable that connects from your modem to the Orbi router in place.

Temporarily, disconnect the Ethernet cable that is NOT connected to your modem and use that port to connect another Ethernet cable from the Orbi router to the Time Capsule WAN "O" port.

Later, when the Time Capsule is set up and working, you can then connect the Ethernet cable that you disconnected temporarily before.....to any one of the three LAN <--> Ethernet ports on the back of the Time Capsule. Now, you will still have an additional two Ethernet ports on the back of the Time Capsule for other additional Ethernet devices that you might want to connect in the future.

Note that you will still need an additional Ethernet cable to connect from the Ethernet port on the Orbi router to the WAN "O" port on the Time Capsule.

Post back when you are ready to proceed.

Another option......more expensive and more complicated.......would to purchase a 5 port Ethernet switch and connect the switch to the Ethernet port on the back of the Orbi router. In effect, this will give your Orbi router 4 more Ethernet ports instead of only one.

Then, connect your other Ethernet device......that you temporarily disconnected before......to the 5 port switch and also connect the Time Capsule to the switch.

Netgear makes excellent 5 port Ethernet switches. Make sure that you get a Gigabit Ethernet switch if you decide to go the more complicated path.

Is it possible to use the modem provided by the internet provider and netgear router and a time capsule?

Sure.

Your next question might be "how" to do this. If that might be the case, we need some additional information from you:

1) The model number of Netgear router that you have

2) Whether you will be using a Mac, a PC, or an iPhone / iPad to set things up

I assume that the Spectrum modem and Netgear router are already hooked up and operating normally, correct?

No need to do anything to your Spectrum modem and Netgear Orbi mesh system. Leave them connected as they are now, powered on and operating normally.

As it stands now, you already have one wired Ethernet cable connection from the modem to the WAN Ethernet port on the back of the Netgear router.....and there is another free LAN <--> Ethernet port on the back of the Netgear router.

To summarize, you will be........

1) Connecting another Ethernet cable.....which must remain permanently connected......any length will do..... from the other free LAN Ethernet port on the back of the Orbi router to the WAN "O" (circle of dots) port on the back of the Time Capsule.

2) Performing a Hard Reset on the Time Capsule to erase the current network settings......so the Time Capsule can be reconfigured to pick up the new settings that it needs from the Orbi router. This type of reset will not affect any of the data that might already be stored on the Time Capsule hard drive.

3) Configuring the Time Capsule to create a wireless network using the AirPort Utility setup "helper" or "wizard". Later, if you don't need another Wi-Fi network for guests or the kids to use, you can turn off the WiFi function on the Time Capsule if you wish. More on that later.

Post back when you have the Ethernet cable that you will use with the Orbi router and Time Capsule.......(we assume that you have already tested the Ethernet cable to make sure that it is working correctly)...... and you are ready to proceed.

Nice work! Happy to help.