If the final state contains three particles, solar neutrinos exhibit a continuous spectrum; if it's only two products, the solar neutrino spectrum is a discrete line. That's just energy and momentum conservation. The reaction you point out is
$e^-+{}^7\mathrm{Be}\rightarrow {}^7\mathrm{Li}+\nu_e$
But the ${}^7\mathrm{Li}$ has an energy state that is accessible in this decay; from the iaea.org Live Chart of Nuclides:

The lowest 477keV energy state is accessible, so the de-excitation gamma from that may carry those 477keV away. Hence, two discrete neutrino energies are possible with either 0.86MeV or 0.38MeV.