$M_{2,4}$ is the space of $2\times 4$ matrices: $\dim = 2\times 4 = 8$. $P_2(t)$ is the space of polynomials of degree $\leq 2$: $\dim = 3$. Therefore $\dim\text{Hom}(M_{2,4}, P_2(t)) = 8\times 3 = \mathbf{24}$.