A Mongoose bike has back brakes that are similar to those on a ten-speed. A front handle pulls a cable attached to a bolt inside a yolk-style harness. This pulls the two back brakes together and applies pressure to the wheel rim. The brakes generally function very well, but can break after a lot of use. One common problem is the loosening of the brake wire. This can be fixed with a few basic tools.
Depress and then release the back brake handle bar lever. You will see the brakes clamp down on the wheel rim. Adjust them according to their current position. For example, if the left one clamps down sooner, then push the yolk to the left.
Loosen the back bold on the yolk harness right over the center of the back brakes using a ratchet or Phillips head screwdriver (depending on your model). Give it a quarter turn or less to loosen the bolt and allow the yolk to freely move right or left.
Reposition the brake yolk so both arms are positioned equidistant from the tire rims. Then tighten the harness down again until it is secure.
Retest the brakes by pulling on the handle bar lever. The two brake arms should clamp down on the wheel rim at the same time. If not, repeat steps 2 and 3 until the arms are positioned properly.