The electron emits a photon, propagates as a virtual electron, then annihilates with the positron to produce the second photon. Related to the Compton s-channel by crossing.
The computational chain
From diagram to number—every step of the amplitude calculation.
The diagram
The electron emits a photon at vertex 1, propagates as a virtual electron with momentum $p - q_1$, then annihilates with the positron at vertex 2 to produce the second photon.
Feynman rules expression
$$i\mathcal{M}_t = (-ie)^2\,\epsilon_\mu^*(q_1)\epsilon_\nu^*(q_2)\,\bar{v}(p')\gamma^\nu\frac{i(\not{p}-\not{q}_1+m)}{(p-q_1)^2-m^2}\gamma^\mu u(p)$$
The structure is related to Compton scattering by crossing: replace the incoming photon with an outgoing photon and the outgoing electron with an incoming positron. The Mandelstam variables remap: what was $s$ in Compton becomes $t$ here.