Finding collisions for the DES F-function
If S is a DES S-box, for a given "output", S(input) = output has exctly 4 solutions for "input", or "collisions". You can then find collisions for F by concatenating collisions for each S-box.
You can start with setting an output for F and then look for all possible "inputs" for each of the 8 S-boxes on the 4 relevant bits of the output of F.