The applied force of a 2.0-kg object is 8.4 N [E] and the friction is 2.2 N [W]. What is the motion of the object?

Can I use the formula Fnet = ma?

Yes, but first add the two force vectors. The acceleration will be in the same direction as the resultant force.

The magnitude of the resultant force is
sqrt [(8.4)^2 + (2.2)^2] = 8.683 N