How do I add an additional submit handler in commerce checkout form?
What you are doing is correct.

The problem is that Drupal Commerce has defined the submit action on the buttons that is clicked, which will be used instead of the submit handlers defined on the form itself. So you need to add your submit handlers to the buttons (Cancel, Continue) that you want to use your submit function.

$form['buttons']['continue']['#submit'][]='c_coupon_review_submit';