The speed of light in a transparent plastic object is the same as that in water. Explain whether or not you can see this object when it is submerged in water.

Hello!
Theoretically, the answer is no, you cannot see such an object in water.
It would be no refraction of light between such plastic and water. Refraction occurs when an inclined ray approaches a boundary between two media, in which the speed of light is different.
Refraction occurs because while one side of the ray moves through the external medium, the second side of the ray already hits the internal medium and moves with the different speed. Therefore the front of the ray rotates and the ray itself changes its direction.
If speeds of light are the same, this change of direction is zero (no change of a direction). In other words, all light rays will go through the object the same way as through water, an we couldn't discover it with the help of light. This means we cannot see the object.