Does Verizon FiOS ---coax--- ECB6200 Adapter ---RJ45--- own router ----- desktop works?

Hello,

I am wondering if  

Verizon FiOS ---coax--- ECB6200 Adapter ---RJ45--- own router ----- desktop works?

I have coax in my house.  However, my own router only has RJ45, not coax.    How to get my own router work without Verizon router?   Is this a coax <----> RJ45 question?   What is your recommendation?    Thank you.