x²:x-4=16:x-4

To solve the proportion \( \frac{x^2}{x - 4} = \frac{16}{x - 4} \), we can cross-multiply, which gives us:

\[ x^2 (x - 4) = 16 (x - 4) \]

Next, we can simplify by dividing both sides by \( x - 4 \), provided \( x \neq 4 \) (to avoid division by zero):

\[ x^2 = 16 \]

Now, we take the square root of both sides:

\[ x = 4 \quad \text{or} \quad x = -4 \]

However, we must remember that \( x \) cannot be equal to 4, as we divided by \( x - 4 \) earlier. Thus, the only valid solution is:

\[ x = -4 \]

So, the solution to the equation is

\[ \boxed{-4} \]