Solve the Complex Equation: Balancing Fractions to Find X

Let's solve for $x$ step by step:

First, we rewrite the given equation:
$6 - \frac{3}{8}x + \frac{6}{24}x = \frac{5}{8}x + 7 - 3$.

Simplify the terms:
$\frac{6}{24}x$ simplifies to $\frac{1}{4}x$.

Rewrite the equation:
$6 - \frac{3}{8}x + \frac{1}{4}x = \frac{5}{8}x + 4$.

Convert $\frac{1}{4}$ to $\frac{2}{8}$ to combine the terms:
$6 - \frac{3}{8}x + \frac{2}{8}x = \frac{5}{8}x + 4$.

Combine like terms on the left:
$6 - \frac{1}{8}x = \frac{5}{8}x + 4$.

Move all terms involving $x$ to one side and constants to the other:
Subtract $\frac{5}{8}x$ from both sides:
$6 - \frac{1}{8}x - \frac{5}{8}x = 4$.

Combine the $x$-terms:
$6 - \frac{6}{8}x = 4$.

Simplify $\frac{6}{8}$ to $\frac{3}{4}$:
$6 - \frac{3}{4}x = 4$.

Subtract 6 from both sides to isolate the term with $x$:
$-\frac{3}{4}x = 4 - 6$.

Solve the constant:
$-\frac{3}{4}x = -2$.

Divide both sides by $-\frac{3}{4}$ to solve for $x$:
$x = \frac{-2}{-\frac{3}{4}} = \frac{-2 \times 4}{-3} = \frac{8}{3}$.

Therefore, the solution to the equation is $x = \frac{8}{3}$.