The longer leg of a right triangle is 4 more than twice the shorter leg. the hypotenuse is 4 less than three times the short leg. what is the value of the hypotenuse?

Let the shorter leg = x

shorter leg =x 
longer leg = 2x + 4
hypotenuse = 3x - 4

Given that a² + b² = c²

x² + (2x + 4)² = (3x - 4)²

Remove brackets : (a + b)² = a² + 2ab + b²:
x² + 4x² + 16x + 16 =  9x² - 24x + 16

Moved all terms to the left:
x² + 4x² + 16x + 16 - 9x² + 24x - 16 = 0

Combine like terms:
-5x² + 40x = 0

Multiply all terms by -1:
5x² - 40x = 0

Take out 5x as common factor:
5x(x - 8) = 0

Apply zero product property:
5x = 0 or x - 8 = 0

Evaluate:
x = 0 or x = 8

Since length cannot be zero, shorter leg = 8

shorter leg = 8
Hypotenuse = 3(8) - 4 = 20

20 units