problem similar to DLP
The standard way to prove this problem is at least as hard as the DLP problem is to show that, with an Oracle that can solve this problem, you can solve the DLP problem.

Here's how to do that (and we'll assume that the Oracle will solve random instances with nontrivial probability):

Given the DH problem $G^x = H$, find $x$, we pick random values $s_1, s_2, s_3, s_4$, and form the problem:

$$(G^{s_1})^{r_1} \cdot (G^{s_2})^{r_2} = (G^{s_3})^d \cdot (H^{s_4})$$

This is a random instance, and so the Oracle gives us, with nontrivial probability, values $r_1, r_2, d$, and so we know that:

$$s_1r_1 + s_2r_2 \equiv s_3d + xs_4 \pmod{p-1}$$

We know everything other than $x$ in the above equation, we solve it, and our work is done