Answer
1.8 $\times 10^{38}$ neutrinos are produced per second
Work Step by Step
The reaction that takes place in the sun produces 2 neutrino per reaction as shown by the reaction below.
$4^{1} \mathrm{H}+2 \mathrm{e}^{-} \rightarrow^{4} \mathrm{He}+2 \nu+6 \gamma$
The Rate of neutrino production $R_{\nu}$ is given by
$R_{v}=\frac{2 P}{Q}=\frac{2 \times 3.9 \times 10^{26} \mathrm{W}}{26.7 \mathrm{MeV} \times 1.6 \times 10^{-13} \mathrm{J} / \mathrm{MeV}}=1.8 \times 10^{38} \mathrm{s}^{-1}$
