We do not have any independence assumptions:
$$
P\left(H \mid E_1, E_2\right)=\left(P\left(E_1, E_2 \mid H\right) P(H)\right) / P(E 1, E 2)
$$
So we need to know these probabilities: $P(H), P\left(E_1, E_2 \mid H\right)$ and $P\left(E_1, E_2\right)$, which is B.