The only solid that could have exactly two planes of symmetry is the square prism. Here option A is correct.
A square prism: A square prism has two planes of symmetry. One plane passes vertically through the center of the prism, and the other plane passes horizontally through the center of the prism.
B. Cylinder: A cylinder has no planes of symmetry. No matter how you slice it, the two halves will not be identical.
C. Pentagonal pyramid: A pentagonal pyramid has one plane of symmetry. This plane passes through the apex of the pyramid and bisects the base.
D. Triangular prism: A triangular prism can have zero, one, or two planes of symmetry, depending on the shape of the base. If the base is equilateral (all sides equal), then the prism will have two planes of symmetry. However, if the base is isosceles (two sides equal) or scalene (all sides different), then the prism will only have one plane of symmetry, or none at all. Here option A is correct.