Yes, it works with the Verizon modem. You just need to set the r6300 on a different subnet. I.e. if the Verizon modem is set to 192.168.1.1 (it usually is), you set the r6300 on 192.168.2.1 to avoid conflict. The r6300 will be connected to one of the 4 ports on the Verizon modem and will be assigned an address automatically by the Verizon modem on the 192.168.1.x subnet. The r6300 will then take the Internet signal and create its own network with it in the 192.168.2.x subnet and all the devices you connect to it will be assigned a 192.168.2.x I.p. address by the r6300. Even thou you will still see the Verizon wifi network, you will connect from now on to the netgear one. You can disable the Verizon wifi antenna if you wish but I don't recommend it. If for whatever reason you have a service issue, it's convenient to still be able to connect to the main network and troubleshoot for issues.
Actually you need to ask yourself if you have Verizon DSL or Verizon FiOS. If you have DSL, then the above is probably true, however if you have FiOS you need to get in contact with a level III Support person and very politely and professionally ask them to convert your ONT from Ethernet over MoCA to Ethernet over Ethernet. Then what you do is connect the Actiontec (Stock Verizon Router) up to the ONT's Coax output port, Reset the Subnet to 192.168.1.1 or anything other than 192.168.0.1. & Disable the DHCP (Router Module) since this is just going to be a CoAX Video Switch in the event you have Verizon FiOS TV (If you do not have TV Services you can remove your Verizon Actiontec all together. & just plug in your netgear.