Use the break-pane and join-pane commands. Refer to man tmux for details, options and usage.
Hide Pane 3:
Select pane 3 and enter Prefix-:break-pane -dP.
tmux will send pane 3 to a window in the background (the -d flag) and print some information about it in pane 2 (the -P flag). By default you'll see something like 1:2.0 (meaning: session:window.pane). Hit q to continue working.1
1With some practice you you will be able to drop the -P flag since you can predict the session:window.pane triplet: session defaults to the current session and pane defaults to 0 while window will be the next free window identifier.