Calculating outs problem

[donnybaker]

so if you hold 5c 6c and the flop comes Jc 7d 3c then...

You have 4 outs to the straight: all the 4 cards in the deck.
Independant of that, you also have 9 outs to the flush.
If your read is that either a straight or a flush will beat the opponent. then you have 12 outs (not 13, since the 4c is in both groups). Roughly that's a 24% chance to hit on the turn and another 24% chance to hit on the river.

8 outs to the straight right, or am I missing something (I'm very new at this as well)?

This one's a gutshot. Only a 4 makes the straight.