Let A and B be two finite sets with m and n elements respectively....

We know that, the total number of subsets of a set having $n$ elements is ${2}^{n}$.

$⇒ {2}^{m} - {2}^{n} = 56$

$⇒ {2}^{n}\left({2}^{m - n} - 1\right) = {2}^{3} \times 7$

$⇒ {2}^{n} = {2}^{3}$ and ${2}^{m - n} - 1 = 7$

$⇒ n = 3$  and ${2}^{m - n} = 8$

$⇒ n = 3$ and $m - n = 3$

$⇒ n = 3$ and $m = 6$

Distance between $P\left(6, 3\right)$ and $Q\left(- 2, - 3\right)$ is given by,

$PQ = \sqrt{{\left(6 + 2\right)}^{2} + {\left(3 + 3\right)}^{2}}$

$⇒ PQ = \sqrt{{8}^{2} + {6}^{2}}$

$⇒ PQ = \sqrt{100}$

$⇒ PQ = 10$ units