I am trying to prove that: $$\hom_{\Bbb{F}G}\left(\bigoplus_iV_i ,\bigoplus_jW_j\right)\cong\bigoplus_i\bigoplus_j \hom_{\Bbb{F}G}(V_i,W_j)$$
But I am confused about the meaning of, even: $$\hom_{\Bbb{F}G}(V_1,W)\oplus\hom_{\Bbb{F}G}(V_2,W)$$ On what and how do the elements of thus space act (in both the internal and external interpretations of the direct sum)?