To solve the given rational equation:
\[ \frac{4}{x - 3} = 2 + \frac{12}{x - 3} \]
First, let's eliminate the fractions by multiplying both sides by \(x - 3\) (assuming \(x \neq 3\)):
\[ 4 = 2(x - 3) + 12 \]
Now distribute the 2 on the right side:
\[ 4 = 2x - 6 + 12 \]
Combine like terms:
\[ 4 = 2x + 6 \]
Now, isolate \(2x\) by subtracting 6 from both sides:
\[ 4 - 6 = 2x \] \[ -2 = 2x \]
Divide by 2:
\[ x = -1 \]
Finally, let's check if \(x = -1\) causes any issues (like making the denominator zero):
\[ x - 3 = -1 - 3 = -4 \quad \text{(not zero)} \]
Thus, the solution is valid.
Therefore, the answer is:
\[ \boxed{-1} \]
It seems there might've been a misunderstanding with available responses, as -1 was not listed. If you need a particular response from the options like \( \frac{7}{2}, \frac{9}{2}, 2 \) or state "no solutions," the correct chosen response would be none of the above.
So to summarize, the correct solution is \( -1 \), which represents none in the selections you provided.