This net is to be folded into a standard die, on which opposite faces add up to 7. Which number must be written on the square marked Q?

In the row 2 4 Q 3 the squares one apart are opposite, so Q is opposite 2 and must be $7-2=5$. P and 6 stick out from the row on opposite sides, so P is opposite 6 and is 1. (4 and 3 are already a pair adding to 7.)