For someone who is very new to the mechanics of punching, a left Straight Punch-right Straight Punch-left Hook-right Uppercut combination may be a bit too complex to put together in a smooth, fluid manner.
This is due to the fact that this combination requires you to transition your momentum from one direction to another rather quickly — first forward with your Straight Punches, shifting to the side to deliver your Hook Punch, then pulling up the shoulders to throw your Uppercut. To accomplish all those punches, you have to alternate your legs and hips from left to right the entire time.
It will take time and a lot of practice in order for you to break down these skills into separate components in such a way that will allow your brain a chance to absorb and organize the variety of complex movements. If your body was a car, your brain would be the steering wheel, accelerator, brake, and turn signals all rolled into one. Your brain must first grasp the techniques and combinations before your body can perform them well.
Don't be alarmed! You will coordinate left and right with the top and bottom without having to think about it too much. Being in tune with your breathing is very helpful. It's kind of like playing the drums. The feet and hands are doing two separate things. With practice, all limbs will become coordinated in the correct manner and will work together nicely.