Will give brainliest to first answerer

Let's plug in each coordinate and see what we get:

(2, 0, 0)
-> 2A + 0 + 0 = D
-> 2A = D
-> A = D/2

(0, 6, 0)
-> 0 + 6B + 0 = D
-> 6B = D
-> B = D/6

(0, 0, 5)
-> 0 + 0 + 5C = D
-> 5C = D
-> C = D/5

plugging this back into the equation:
(D/2)x + (D/6)y + (D/5)z = D    [then divide through by D]
(1/2)x + (1/6)y + (1/5)z = 1
and since we have to have integer coefficients, 
multiply through by 30

so we get
15x + 5y + 6z = 30

Second question

Take a look at the bottom-left point in the picture.
If you move three points in the y-direction, you'll reach to the  point A.
 If you instead move up 4 points (or in the z-direction), you reach D.
And finally, if you walk back to point F from point E, you'll have moved back 4 points in the x direction. 

This gives us our measurements, or dimensions: 3 x 4 x 4.
If this were a rectangular prism, the dimensions would just be each of them multiplied.
 But since it's triangular, you need to divide it by two. That gives you a total volume of
(3x4x4)/2 = 24.