Solution
= Solution
Both sides are antisymmetric in $j,k$ and in $p,q$. If either pair has equal indices, both sides vanish. It therefore suffices to take $j\ne k$ and $p\ne q$. The sum over $i$ is nonzero exactly when $(p,q)=(j,k)$ or $(k,j)$; it is respectively $1$ or $-1$. This is exactly
$$
\boxed{\epsilon_{ijk}\epsilon_{ipq}
=\delta_{jp}\delta_{kq}-\delta_{jq}\delta_{kp}},
$$
the <contraction of two Levi-Civita symbols>.