how can it be that the net force exerted on the mass m2 be zero?
At least describe the problem a bit. And why you think the net force on m2 is zero.
Look at the pulleys and the position of the rope.
When you pull the rope, the rope will exert force 45 degrees down to the left by the upper pulley. The next pulley will counterforce with same force 45 degrees up to the right.
You could likely take away the pulleys and shorten the rope....and save some money.
because that is the answer and that's troubling me.could you say that it is incorrect?
No, it's correct. Assuming there's no friction between m1 and m2, the net force on m2 will be zero. See Low-Q's post for details.
If you still have trouble seeing this, trying listing all the forces acting on m2. (Realize that the pulleys are attached to m2.)
Separate names with a comma.