While two forces act on it, a particle is to move at the constant velocity = (2.15 m/s) - (-4.16 m/s). one of the forces is 1 = (2.09 n) + (-6.18 n). what is the other force?

The only way a particle can move at any constant velocity is
if there are NO forces acting on it, or if the forces acting on it
are BALANCED.  That is, all the forces on it add up to zero.

I'm going to assume that the peculiar way you've written your
numbers means that you're writing their x- and y-components.

So, if Force-1 is (2.09N)horizontal + (-6.18N)vertical,
and Force-2 needs to balance out Force-1, then
Force-2 = (-2.09N)horizontal + (6.18N)vertical .

Answer sample (c); // would be best because the percentage of the energy in an incident wave that remains in a reflected wave from this material is the smallest;