Proving knowledge of a value and computation that uses it
This looks like your typical Schnorr identification protocol. Here $r$ is some secret value, which we could think of as having two public keys $r\cdot P$ and $r\cdot Q$. You'll probably want to assume that the DLPs wrt base $P$ and $Q$ are hard as well, as otherwise Alice could possible solve one of these two for $r$. Let's just assume the group has prime order $n$. 

Now we could proceeds as follows (similar to the questions the @SEJPM referred to):


Bob chooses random $s\in \mathbb{Z}/n\mathbb{Z}$.
Bob sends $(s\cdot P, s\cdot Q)$ to Alice.
Alice chooses random $c\in \mathbb{Z}/n\mathbb{Z}$.
Bob computes $t = (s + cr)\bmod{n}$.
Bob sends $t$ to Alice.
Alice checks that $tP = (s\cdot P) + c(r\cdot P)$ and $tQ = (s\cdot Q) + c(r\cdot Q)$.


If the checks of Alice pass, she will believe that Bob knows the DLP of $r\cdot P$ and $r\cdot Q$. I haven't done a too thorough checking, but the properties of a sigma protocol seem to hold. 

Moreover the secrets must both be equal to $(t-s)c^{-1}\bmod{n}$, so they are the same.