You have the following equation:
4⁽³ˣ⁻⁵⁾ = 256
If you take into account 4=2² and 256 = 2⁸, you can write the previous equation as follow:
2²⁽³ˣ⁻⁵⁾ = 2⁸
Then, you have an equation with two quantities with the same base. It allows you to equal the exponents of both sides and solve for x, just as follow:
2(3x - 5) = 8 apply distribution property left side
2(3x) - 2(5) = 8
6x - 10 = 8 add 10 both sides
6x = 8 + 10 simplify
6x = 18 divide both sides by 6
x = 18/6
x = 3
Hence, the solution for x is x = 3