We are given the equation:

$3xy + 4 = 8y - 2x$

Steps to solve for $x$ in terms of $y$:

1. Move all terms involving $x$ to one side: $3xy + 2x = 8y - 4$

2. Factor out $x$ on the left side: $x(3y + 2) = 8y - 4$

3. Solve for $x$: $x = \frac{8y - 4}{3y + 2}$

Thus, the solution for $x$ in terms of $y$ is:

$x = \frac{8y - 4}{3y + 2}$

Would you like more details on any step or have further questions?

Related questions:

1. How would the solution change if the coefficients were different?
2. Can this expression for $x$ be simplified further?
3. How can we graph the relationship between $x$ and $y$?
4. What happens if $y = -\frac{2}{3}$?
5. How would you solve the same equation for $y$ in terms of $x$?

Tip:

When solving for a variable, always isolate the variable by factoring if possible, and ensure to move like terms to the same side of the equation.