If A and B are two sets such that n(A) = 2 and n(B) = 4 , then the...

$n\left(A \times B\right) = n\left(A\right) \times n\left(B\right) = 2 \times 4 = 8$
$∴$ total number of subsets of $A \times B$ are ${2}^{8} = 256$
For the number of subsets not having more than $5$ number of elements.
The required subsets =total number of subsets$-$(sets having $6$ elements) $-$ (sets having $7$ elements) $-$ (sets having $8$ elements)
$= 256 - \dfrac{8 \times 7}{2} - 8 - 1 = 219$