Where does the in-tank fuel filter go?

First - The fuel lines are probably DOA and need to be replaced. That is why the weighted filter/pickup fell out in the first place.

Ethanol (87) Gas RUINS small engines!

The smaller one is PROBABLY the pickup. If they are the same, use the PRIME BULB to see which way the bubbles are flowing. "TO" the carb is the the line that gets the weighted pickup. Make sure the line is long enough to suck out the last of the gas when the trimmer is at "unusual angles".

Car Guy 451
July 2013