How to detach a tmux session that itself already in a tmux?

I've opened a tmux session on my local machine, and ssh to the remote machine. After this, I typed command "tmux attach" on the remote machine, then I got a remote tmux session on my local tmux session.

Now I want to detach the remote tmux sesstion, I've tried

C-b d

but it detached my local tmux session rather than the remote one.

How can I detach the remote tmux sesstion?

C-b C-b d

(assuming default bindings)

The first C-b is interpreted by your local tmux (because it is the first to see all your keystrokes). The second C-b is a command that causes your local tmux to send a C-b to its active pane; this generated C-b arrives at the remote tmux. The d passes through the local tmux unchanged; when it gets to the remote tmux it triggers the detach command.

1. You type C-b.
   Your local tmux interprets it as the prefix key; nothing is sent to the processes running under the local tmux.
2. You type C-b.
   Your local tmux has it bound to the send-prefix command.
   1. Your local tmux sends a C-b to the process running in the active pane (ssh).
   2. ssh forwards it (through sshd, etc.) to the process running on the remote end (remote tmux).
      Your remote tmux interprets it as the prefix key; nothing is sent to the processes running under the remote tmux.
3. You type d.
   Your local tmux passes it through normally (since the second C-b finished a full command key sequence for the local tmux).
   Your remote tmux has it bound to detach-client; it detaches the active client.

This is the same as when you need to send a C-b to any program running inside a tmux session. If you wanted to send C-b to your normal shell (e.g. because your shell is using Emacs-style editing where C-b is backward-char (and you dislike using the arrow keys)) you would need to use C-b C-b to get a single C-b to the shell.

Another way to do it without worrying about the keybindings making it to the right tmux instance is to type tmux detach in the remote tmux session.