Solve for \( x \) : \[ 2=\frac{10}{x-6} \]

To solve the equation \[ 2 = \frac{10}{x - 6}, \] we start by eliminating the fraction. We can do this by multiplying both sides of the equation by \( x - 6 \): \[ 2(x - 6) = 10. \] Next, we distribute the \( 2 \) on the left side: \[ 2x - 12 = 10. \] Now, we will isolate \( x \) by first adding \( 12 \) to both sides: \[ 2x - 12 + 12 = 10 + 12, \] which simplifies to \[ 2x = 22. \] Next, we divide both sides by \( 2 \): \[ x = \frac{22}{2} = 11. \] Thus, the solution is \[ \boxed{11}. \] To verify, we can substitute \( x = 11 \) back into the original equation: \[ 2 = \frac{10}{11 - 6} = \frac{10}{5} = 2. \] Since both sides are equal, our solution \( x = 11 \) is confirmed to be correct.