**Step 1 — Use the property of a parallelogram.**
In a parallelogram the **diagonals bisect each other**, so the midpoint of $AC$ = midpoint of $BD$.

**Step 2 — Find the midpoint of diagonal AC.**
$$\text{Mid}(AC) = \left(\frac{4+4}{2},\ \frac{5+3}{2}\right) = (4,\ 4)$$

**Step 3 — Find the midpoint of diagonal BD.**
$$\text{Mid}(BD) = \left(\frac{m+1}{2},\ \frac{6+n}{2}\right)$$

**Step 4 — Equate the two midpoints.**
$$\frac{m+1}{2} = 4 \qquad \text{and} \qquad \frac{6+n}{2} = 4$$

**Step 5 — Solve.**
$$m + 1 = 8 \ \Rightarrow\ m = 7$$
$$6 + n = 8 \ \Rightarrow\ n = 2$$

$$\boxed{m = 7,\quad n = 2}$$