Let $$A$$ and $$B$$ be two finite sets with $$m$$ and $$n$$ elements respectively. The total number of subsets of the set $$A$$ is 56 more than the total number of subsets of $$B$$. Then the distance of the point $$P(m, n)$$ from the point $$Q(-2, -3)$$ is

 The number of subsets for a set with $$k$$ elements is $$2^k$$.

 We are given $$2^m - 2^n = 56$$.

 Factor out $$2^n$$: $$2^n(2^{m-n} - 1) = 56$$.

 Prime factorize $$56 = 8 \times 7 = 2^3 \times (2^3 - 1)$$.

 Comparing terms, $$n = 3$$ and $$m-n = 3 \Rightarrow m = 6$$. So, $$P$$ is $$(6, 3)$$.

 Use the distance formula:

$$\text{Distance} = \sqrt{(6 - (-2))^2 + (3 - (-3))^2} = \sqrt{8^2 + 6^2} = \sqrt{100} = 10$$