I've run into this problem a few times and google is utterly useless. Luckily the man page isn't too difficult to read. And documenting this will provide a quick reminder the next time I forget.
The command you're looking for is
You'll have to run it a couple times. I've reindexed the pane numbers to match tmux's convention. Since Pane 0 ultimately borders the other two panes, you should imagine that you're moving Pane 1 (right of 0), and then moving Pane 2 (below Pane 1).
│Pane 0│ PREFIX + : │Pane 0│Pane 1│
├──────┤ move-pane -h -s 1 -t 0 │ │ │
│Pane 1│ ├──────┴──────┤
├──────┤ │Pane 2 │
│Pane 2│ │ │
PREFIX + : │Pane 0│Pane 1│
move-pane -v -s 2 -t 1 │ │ │
│ │Pane 2│
│ │ │
Here are rough keybindings to achieve the same. Just make sure to focus the pane that will move first.
bind-key g command-prompt -p "place below. select target window" "move-pane -h -t %%"
bind-key G command-prompt -p "place right of. select target window" "move-pane -h -t %%"
If you have trouble figuring out the pane numbers, remember that the number is assigned by order, the number doesn't stick with any particular pane. Use a keybinding to display the pane numbers before each movement. The default is
PREFIX + q. If yours is different, you can use
PREFIX + ? to find it.