An atom of an element 'A' has three electrons in its outermost shell and that of 'B' has six electrons in the outer most shell. The formula of the compound formed between these two elements is

In a neutral molecule, the sum of the bonding valance electrons must be 
An atom of an element  A has 3 valance electrons, the 'A' charge will be either +3  and B' atom has 6 valence electrons ,the charge of B will be -2
$3\times \mathrm{A}=-2\times \mathrm{B}$
To be equal, $\mathrm{A}=2$ and $\mathrm{B}=3$

Therefore, ${\mathrm{A}}_2{ \mathrm{B}}_3$