In your first example, you are giving the -c flag to docker exec. That's an easy answer: docker exec does not have a -c flag.

In your second example, your shell is parsing this into two commands before Docker even sees it. It is equivalent to this:

if docker exec [id] cd /var/www/project
then
    composer install
fi

First, the docker exec is run, and if it exits 0 (success), composer install will try to run locally, outside of Docker.

What you need to do is pass both commands in as a single argument to docker exec using a string. Then they will not be interpreted by a shell until already inside the container.

docker exec [id] "cd /var/www/project && composer install"

However, as you noted in the comments, this also does not work. That's because cd is a shell builtin, and doesn't exist on its own. Trying to execute it as the initial command will fail. So the next step is to hand this off to a shell to execute.

docker exec [id] "bash -c 'cd /var/www/project && composer install'"

And finally, at this point the && has moved into an inner set of quote marks, so we don't really need the quotes around the bash command... you can drop them if you prefer.

docker exec [id] bash -c 'cd /var/www/project && composer install'

Everything after the container id is the command to run, so in the first example -c isn't an option to exec, but a command docker tries to run and fails since that command doesn't exist.

Most likely you found this syntax from a docker run command where the entrypoint was set to /bin/sh. However, exec bypasses the entrypoint, so you need to include the full command to run. As others have pointed out, that command includes a shell like bash or in the below example, sh:

docker exec [id] /bin/sh -c 'cd /var/www/project && composer install'

The other answers are fine if you want to run 2 arbitrary commands. But if the first command is simply cd, then you should use the -w option to set the working directory instead.

docker exec -w {dir} {container} {commands}

So in your example:

docker exec -w /var/www/project {container} composer install