[Syl]

The ELECTROLYTIC CONDENSER/CAP 6 mf. -6 mf ., 150v has a red and yellow wire coming from one end and a ground out the other ... the red and yellow are soldered to a resistor and the ground soldered to some type of terminal block ....
Does it need the ground to function ?

This can has two capacitors. The black is the common ground for both capacitors
and the red/yellow are the positives. So you'll need 2* 10uF caps at 250V.

When replacing with two new capacitors, tie both negatives together and solder
where the black wire is. Then use any of the positive to the red and the other positive to the yellow
wire.

Syl