To solve this equation, we need to simplify the expression on the left side and then solve for x.

First, let's simplify the expression inside the brackets:
(4x + 63) ÷ 3 - 105

To divide (4x + 63) by 3, we can distribute the division to each term inside the brackets:
(4x ÷ 3) + (63 ÷ 3) - 105

Simplifying further:
(4/3)x + 21 - 105

Combining like terms:
(4/3)x - 84

Now, let's rewrite the equation:
(4/3)x - 84 * 6 = -480

To solve for x, we'll isolate the variable by moving the constant term to the other side of the equation:
(4/3)x = -480 + 504

Simplifying:
(4/3)x = 24

To solve for x, we'll multiply both sides of the equation by the reciprocal of (4/3), which is (3/4):
x = 24 * (3/4)

Simplifying:
x = 18

Therefore, the solution to the equation is x = 18.