"Modus moron" rule of inference?
It's true that if $P$ is false then $P\Rightarrow Q$ is true. But the question is not asking if $P\Rightarrow Q$ is true, it's asking you if you can infer $P$ from $P\Rightarrow Q$ and $Q$.
Let's be concrete. Suppose "if Mark is drunk, then Mark is happy" is a true statement, because Mark is a happy drunk. Given that Mark is presently happy, may we infer that Mark is drunk? No; there may be other circumstances in which Mark is happy besides being drunk.
(This example is drawn from a real life discussion between friends about putative alcoholism which devolved into a debate about logical implication.)
This pattern is a logical fallacy called Affirming the Consequent, though I often call it Modus Bogus.
To show it is not a valid inference, here is a simple Refutation by Logical Analogy:
If I have blond hair, I have hair
I have hair
Therefore, I have blond hair
Here is my favorite logical fallacy:
$$\frac{}{\therefore P}\qquad \text{(hokus ponens)}$$
Even if affirming the consequent is not valid, other logical rules still work. Other logical rules still work. Therefore, affirming the consequent is not valid?