CainIsmene gave a great answer. I'll just add one more general concept. Particles don't *just* annihlate on their respective antiparticle. First I have to define the conserved quantum numbers:

-charge

-baryon number (number of "matter" baryons - protons, neutrons, and other exotic ones minus number of antiprotons and antinuetrons)

-and lepton number (number of electrons+nuetrinos minus antielectrons and antineutrinos asterix we don't know if antineutrinos exist)

These three things, as far as we know, are perfectly conserved in nature. Now a useful definition of "annihilate": quickly turn into lower mass particles like electrons, muons, pions, or photons with a lot of kinetic energy. Annihilation occurs if you ever bring two particles into contact, and there exists any collection of lower mass particles with the same conserved quantum numbers. There is an important caveat, however, that in some cases two particles don't directly interact, which will stop them from annihilating (like a muon cant annihilate with an anti-electron until the muon decays into an electron, which takes about a microsecond, because there's no direct interaction between the two).
-So an antiproton and a neutron can annihilate because the baryon number of the system is zero and the charge of the system is -1. three pions, two negative charge and one positive charge have the same conserved quantum numbers. And there are plenty of particle interactions that allow that conversion. So they annihilate and make those pions.