Begin the first combination when you are in an opposite stance to your opponent; meaning you have your opposite lead feet forward. Use the hook kick to connect with your opponent's inner thigh. This will draw his attention downwards and also serve to disrupt his balance. Follow the kick with a reverse punch / cross.
In the next combination Lyoto Machida teaches us how to fake a foot sweep and follow with a cross into a flying knee attack. Use to foot sweep with your lead foot to distract your opponent, follow with a reverse punch and then move forward, gaining momentum, to jump into a knee attack.
In the third combination Lyoto Machida demonstrates a cross leading into a hook. The cross is thrown as you are moving forward and is designed more to blind your opponent and draw his guard across his face leaving the opposite area exposed to a hook punch. Notice how the body of the attacker ends in a position making it awkward for the defender to counter if the hook is unsuccessful.
The next combination is similar to the one above. Begin as before, by stepping forward with a cross to blind your opponent and draw his guard. As your step forward lands follow up with a round kick to your opponent's head. The forward step will also open up your hips allowing them to swing back into the round kick, making it that much more powerful.
Next Machida looks at a combination using three techniques. He moves from a cross to a hook to a round kick. As before, the initial cross serves more to blind the opponent than anything else, leaving him exposed to the follow up hook. This technique should be delivered while angling into your opponent. The placing of the rear leg prior to the hook is important for the success of the round kick. By angling your body you are also making it hard for your opponent to counter effectively. After the hook throw a powerful roundhouse kick to your opponent's head.
The next combination uses a more difficult spinning hook kick. Start with a jab followed by a cross. This initial combination is to confuse and blind the opponent, leaving him open for the spinning hook kick to his head for the KO.
For the remainder of the video Lyoto Machida introduces some focus mitt combinations. The first is a jab, cross, hook combo. Notice that both he and his training partner are moving around, practicing footwork and altering the distance each time the combination is executed. The second combo is a cross, hook, cross series. Notice that the first cross is directed to the body of his training partner, taking his awareness downwards. The third combination is a jab, hook, cross one.