This is to do with the conservation of quantum numbers (charge, baryon number, electron number, muon number, and strangeness). In particular for this example, we're trying to find where lepton numbers are (and are not) conserved.
Interaction A:
Charge: Is conserved - an initial charge of zero is countered by a negative and a positive particle, and a neutral particle.
Baryon Number: Is conserved - none of these particles are baryons;
Electron Number: Is conserved - none of these particles are electrons;
Muon Number: Is conserved - the anti-muon's lepton number of +1 is countered by the muon neutrino's lepton number of -1;
Strangeness: Need not be conserved - this is a weak interaction, in which strangeness can (but won't always) change by 1.
You can repeat this process for the other interactions to determine which are possible and which are not.
Hope that helps!