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How To Throw The Cross - The cross is a power punch and it will be thrown with your stronger hand so naturally it will have more power behind it. A common combination to throw is a 1-2, or a jab-cross.
To throw a cross you snap your hips while extending your arm straight out towards your opponent. It's important to use your body and not just your arm when throwing your punches.
If you want to try a more advanced "cross" try learning how to throw a superman punch!
How to Throw A Hook - A hook is also a power punch and comes from the side to hopefully break your opponents guard. A common combination is the 1-2-3, or jab-cross-hook.
The hook can be thrown with your left or right, but in a fluent combination such as the 1-2-3, you usually will be alternating hands. For instance if your a righty you will jab with your left, cross with your right and then hook with your left.
When you hook your elbow is parallel to the floor so your punch is coming from a side angle and is aimed at the ear or chin of your opponent. Make sure to use your hips!