The surface of the prism will be the sum of the bases' area plus the lateral surface area.
Base area is 6*8/2 = 24 in^2. There are two triangles so 2*24 = 48 in^2
The lateral surface area is equal to height times the sides of the base.
7*(6+8+10) = 168 in^2 The hypotenuse of the base triangle is 10 in. I used the Pythagorean Theorem to find it. 6^2 + 8^2 = x^2
36+64 = x^2
x =10 in
Surface area = 48 + 168 = 216 in^2