Q: Will a Airport Time Capsule work with a Motorola SB6782 modem/router?

Yes if you only use the modem. Then the Time Capsule can act as your router. You may need to turn off the modem/router's radio so it does not attempt to create Wi-Fi networks.

Run an Ethernet cable from the Motorola's Ethernet port to the WAN (World) port on the Time Capsule. Connect your computer to one of the free LAN ports for a wired connection. Use Airport Utility to configure the Time Capsule for wireless. Be sure you enable WPA2 security for your Wi-Fi.

AirPort base stations- Setting up and configuring an extended wireless network (802.11n)

See your other post for other answers.  Please, do not double post on the forum....it makes things very confusing.