One side of the moon always faces Earth because the time it takes the moon to spin on its axis is blank the time it takes the moon to travel around Earth.

The word to fill in the blank is "equal". Because the time taken to rotate (spin on its axis) is equal to the time of revolution (going around the earth), this means that both have the same rate of angular rotation. So for every bit that the moon goes around its orbit around earth, the moon itself rotates accordingly to present the exact same side to earth.