Where does the return fuel line go on a Honda GX610. Mine is missing and I can not find where it goes,

Gravity feed tank need no fuel pump.....

There are two hoses, the fuel hose which has the filter on the end in the fuel tank, and a return to tank hose, the fuel hose goes to the lower of the two connections on the carb, the return to tank hose ( which is normally clear ) goes to the higher connection on the carb

Fuel goes through fuel filter in tank to carb to purge bulb and back into tank.

Plugged fuel tank pickup filter is a possibility.

if the fuse pops when turning to crank position the problem lies within the small solenoid wire to the starter (this wire goes from the ign.switch to the starter solenoid and is powered up when in the start position) this wire is shorted to ground....or the starter solenoid is shorted....best way to tell is unhook wire from solenoid and turn key to start...if the fuse does not pop its the solenoid....do this several times to verify

i can help you what do you need to know

Try search for a return line for your make and model, or go to a local Honda shop.

Goto smallenginewarehouse.com there u will get your specs

The gas lines probably broke because of the ethanol-laced gasoline we have to use nowadays. It deteriorates them. If the unit has the external purge/primer bulb, the way mine did, it is not that hard. Just remember...the primer bulb "pulls" fresh fuel from the fuel tank to and thru the carb, thus pushing out any air/old fuel in the metering chamber of the carb back to the fuel tank in the return line...that said..
Fuel tank...2 lines...smaller diameter line goes directly to the carb body. There are probably 2 brass nipples on the carb. This line goes to the one on the body opposite the end of the carb with the vent-hole in the cover. This is the fuel pump end...where fresh gas enters the carb.
The larger line out of the fuel tank connects to the longer nipple on the purge/primer bulb. This is the fuel return line.
The remaining fuel line (larger diameter) goes from the vented-cover (has writing on it) end of the carb to the shorter nipple on the purge/primer bulb. This line carrys air and old fuel OUT of the carb to the bulb where it is then PUSHED back to the fuel tank via the return line...so you have a small diameter supply line to carb...an intermediate larger diameter line from the carb to the bulb and finally the larger diameter return line from the bulb BACK to the fuel tank.
Go to a small engine shop and purchase about a foot each of the 2 different diameter fuel lines needed and install those new "Tygon" fuel lines as your fuel line replacement.