Where do these cables hook up? Fuel system solenoid

First we need the equipment and engine model numbers so can look up the wiring diagrams.
 
Second if you are referring to fuel on the bottom of the carburetor the n don't understand the purpose of it. It is only a device to prevent after fire boom as you shut down the engine. It doesn't prevent a leaky float valve from filling the crankcase wit h fuel. This is a misconception many DYIers have about what the function of this device.

Still need the model number of the Snapper. As those wire may or may not need to be connected. Could be for optional equipment add-ons.
 
With you changing out easily fix 100 to 150 usd carburetor I assume you went with one of those off the wall Chinese clone carburetors. Hope you got one that is properly jetted. My cost before shipping of the current 799727 OEM carburetor is 97.24 before shipping costs. Of course the previous carburetor may had been a one wire fuel solenoid and the carburetors currently supplier are two wire versions. This means you need to make up a new two wire connector and terminals where you get +12v and ground to the solenoid when the ignition switch is on and during starting.
 
Btw I rarely ever need replace a carburetor; unless, either the owner has damage it beyond repair or it is severely corroded. So far this year I have replace one carburetor out the 100 that I repaired. Even then it was a Stihl Zama carburetor with a bad main nozzle.

Originally that mower came with either a 8 or 10 hp engine but here is the wiring diagram for the mower body. Ifthe mower still has the original keyswitch it will need upgrading to operate the fuel solenoid and additional wiring will be required to connect the fuel solenoid.