You've got a typo. You're missing the argument definition for the defun. In this case, since the function my-c-mode-common-hook doesn't take any argumentr, add an empty set of parens after the function name.

(defun my-c-mode-common-hook ()
    (define-key c-mode-map (kbd "C-<f12>") 'compile))
(add-hook 'c-mode-common-hook 'my-c-mode-common-hook)

You've got a typo. You're missing the argument definition for the defun. In this case, since the function my-c-mode-common-hook doesn't take any arguments, add an empty set of parens after the function name.

(defun my-c-mode-common-hook ()
    (define-key c-mode-map (kbd "C-<f12>") 'compile))
(add-hook 'c-mode-common-hook 'my-c-mode-common-hook)