If for every force there is an equal and opposite reaction force, how is it possible for an object to accelerate

By the use of the reaction force one body is able to accelerate because it is not fixed to a rigid support which offers a materialistic resistance.

Explanation:

For every  force there is an equal and opposite reaction is stated in the Newton's third law of motion holds true universally.

This law accounts for the acceleration of the bodies with respect to the object that applies force on the other body. The acceleration is possible when iether one of the body is fixed and cannot move or when that both the bodies are not fixed can move.

This is in accordance with the Newton's second law of motion, stating that the Force is directly proportional to the rate of change in momentum.