1. Use the formula for number of subsets

If a finite set has $k$ elements, then the total number of subsets is: $2^k$

So for sets $A$ and $B$:

• Number of subsets of $A = 2^m$
• Number of subsets of $B = 2^n$

Given: $2^m = 2^n + 56$ or $2^m - 2^n = 56$

2. Factor the expression

Assume $m>n$ (since $A$ has more subsets than $B$): $2^n(2^{m-n}-1)=56$

Now, $56 = 2^3 \cdot 7$

Since $2^{m-n}-1$ is odd, it must divide the odd part of $56$, i.e. $7$.

Thus: $2^{m-n}-1=7$ $2^{m-n}=8=2^3$ So, $m-n=3$

Then: $2^n \cdot 7 = 56$ $2^n=8$ $n=3$

Hence: $m=n+3=6$

So the point is: $P(m,n)=(6,3)$

3. Find distance from $Q(-2,-3)$

Distance formula: $PQ=\sqrt{(6-(-2))^2+(3-(-3))^2}$ $=\sqrt{8^2+6^2}$ $=\sqrt{64+36}$ $=\sqrt{100}$ $=10$

4. Check options

The correct option is: $\boxed{10}$ So, Option B is correct.