It's intended to be part of the challenge to figure that out (you can often reason that it's impossible to move blocks between most puzzles), but in case you want a more specific answer:
SPOILERS BELOW
I believe there is only one normal puzzle solution that requires smuggling a block and it's quite obvious because you can't do anything at all in the next puzzle without it. However, many of the secret buttons require a bit of block smuggling to reach them.