What is the lateral surface area of a right hexagonal prism whose base is a regular hexagon with sides measuring 8 inches long and altitude measuring 6 inches tall?

Assuming your "altitude" is the height of the prism--the distance between bases, the lateral area is the sum of the areas of the six rectangular faces. Each of those has an area of ...

(8 in)(6 in) = 48 in^2

so the 6 of them will have an area of ...

lateral area = 6×48 in^2 = 288 in^2

_____

Comment on nomenclature

'Altitude' is usually associated with the height of a triangle. In the case of a regular polygon, the 'altitude' of a triangular section of the polygon is called the 'apothem', and is often designated using the letter 'a'. If the polygon is regular, the apothem can be calculated from the side length and the number of sides, but it is often given in problems involving area, perimeter, and/or volume.

The distance between the parallel bases of a prism is often referred to as the prism height or length. The use of the word 'altitude' is confusing in this case.

Since the lateral area is the product of the perimeter of the base and the distance between bases, we have to assume that your 'altitude' refers to the distance between bases. Otherwise, there is not sufficient information to work the problem.