My question is am I able to connect:
Actiontec t3200m coax as an output to coax to a upstairs router with coaxial input to ethernet cable?
Any special thing I need to do aside from buying a router with coaxial input?
Yes, the coax can be used on the T3200M. There are settings in the admin web interface to manage it. At the other end, you will need a MOCA adapter to connect the coax to Ethernet for the rest of your network.
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If your plan is to add another router you should do a bit of research on this first to know what you are getting into. There have been a number of discussions here in the Neigbourhood on the correct topology, required settings and caveats (especially if you have Optik service).