Broken potentiometer on old computer speakers
Each triple of pins should be (input signal, wiper, ground). Wiring signal to wiper should give the full signal with no attenuation, and you can ignore ground (or wire a 10K resistor between the wiper pin and the ground, which will be more exactly what the pot would be doing). The two triples are of course for the left and right channels. Assuming the connected pair is ground, just wire the other two of each triple together -- the blue bars I've added to your photo here show where your jumps need to be.



The potentiometer's full resistance between the input signal and ground is split by the moving wiper; the split resistance forms a voltage divider that reduces the input signal voltage by a ratio. 

If you find that 100% volume is louder than you like, you can wire resistors signal-to-wiper and wiper-to-ground; only the ratio between them matters to the volume, though you'll want to keep the total somewhere in the 10K-ish magnitude (anything between 5K and 20K is probably fine).