"Puzzle Time" does not exist in Tony Hawk's Project 8. You are confusing it with Tony Hawk's Underground (THUG) and THUG 2, which feature the "Puzzle" goal type (collect letters S-K-A-T-E, C-O-M-B-O, etc., in a specific order within a time limit).
Play Tony Hawk's Underground 1 (2003) or THUG 2 (2004) on PS2, Xbox, GCN, PC, GBA. They have explicit "Puzzle" goals in each level. Project 8 (2006) shifted to "Nail the Trick" physics focus.