No matter how careful you tend to be, sometimes you slip and make mistakes that hurt your wife. Being a real man doesn't mean you should never make your wife angry because it is bound to happen at some point.
Here are things you should do to calm her down when she is mad at you.
1. Apologise
Apologising is the very first step to calming your wife down when she is angry with you. Saying "sorry" doesn't mean you are a weak man, it means you are mature and you value your marriage.
It is absolutely the right thing to do especially if you are in the wrong. Accepting your mistake is the best thing you can do at this moment and apologising will calm her down.
2. Try to solve the problem
If the problem is solvable then please try to fix it. If it isn't, acknowledge your mistake and promise her you'll never repeat it. The worst thing you can do at this time is to walk out of her or stay silent.
Say something, don't keep quiet and don't leave her alone with the anger unless she insists you leave her alone.
3. Do something she likes
After she has forgiven you, you can do something she likes like hugging her from behind if she loves it, carry her around the house or prepare her favourite dish. Just do anything as long as she will become happy when you do it.