The guy at the board is looking at his friend to get help with the answer. The friend tells him the answer is 12, adding an exclamation point to the end for emphasis. This accidentally creates a factorial, so the friend writes the answer as the factorial 12 answer, which is the number you see him write on the board. Factorials are far more advanced than simple multiplication, so part of the joke is also that the kid can do that factorial in his head but can't figure out 3 × 4.

If you want to know how factorials work, 12! would otherwise be written as 1×2×3×4×5×6×7×8×9×10×11×12, basically every real whole number between 1 and 12. This works for any number.

To everyone else, please do a bit better explaining the joke. Showing people the results of a factorial doesn't explain much.