Final answer:
The volume of the prism with a right triangular base and dimensions given is 288 cubic centimeters.
Step-by-step explanation:
The volume of a prism is found by multiplying the area of the base by the height of the prism. The base is a right triangle and the formula to calculate its area is 1/2 × base × height. For the given dimensions, the base is 8 centimeters and the height is 6 centimeters, so the area of the triangle is 1/2 × 8 cm × 6 cm = 24 cm². The height of the prism is 12 centimeters. Therefore, the volume of the prism is the area of the triangle times the height of the prism: 24 cm² × 12 cm = 288 cm³.