When two dices are thrown simultaneously, the total number of combinations of the number that will be shown on faces of both the dices is given by,
${\color{Magenta}{(1,1)}},(1,2),(1,3),{\color{Blue}{(1,4)}},(1,5),(1,6)$
$(2,1),{\color{Magenta}{(2,2)}},(2,3),(2,4),(2,5),(2,6)$
$(3,1),(3,2),{\color{Magenta}{(3,3)}},(3,4),(3,5),(3,6)$
${\color{Blue}{(4,1)}},(4,2),(4,3),{\color{Magenta}{(4,4)}},(4,5),(4,6)$
$(5,1),(5,2),(5,3),(5,4),{\color{Magenta}{(5,5)}},(5,6)$
$(6,1),(6,2),(6,3),(6,4),(6,5),{\color{Magenta}{(6,6)}}$
$\implies$ Squares of all integers are known as perfect squares.
$P(E)=\dfrac{n(E)}{n(S)}$
$\implies P(E)=\dfrac{8}{36}=\dfrac{2}{9}$
So$,(B)$ is the correct answer.