When the vehicle it in motion, when applying brakes the vehicle pulls either right or left what is the problem?

There are quite a few things that may be causing this:

first of all this is related to any one or more of these; Tires, brakes (ABS/non ABS), suspension, etc.

It should not be too hard to know: first lok at wheels and check condition. if they are in very bad condition you should probably change them as this alone is a risk.

Next i would check for any suspension problems. does the car stand level on all corners? as in is there any obvious different in height of any corner of the car? if there is there might be a broken suspension. check stiffness at each end by pressing down on car. there should be equal back pressure when pressing down on the right and left corners. Check for leaks in the suspension arms. if there is an oil leak then probably you need to change this part. the brakes part are tricky. they might look good but when applying themthey are bad. so the best way is to look for visual damage on the brake capilars and plates. the brake plate should be like a mirror with no scratches.

if there are deep scratches then you need to check with your mechanic. and lastly to be sure you should double check your steering column components and make sure your steering wheel and your wheels alignment. They should both point exactly straight and there should no gaps in the steering wheel when the car is off.

Let a mechanic check it but i think i covered all possible scenarios. hope it helped!