1. **State the problem:** We need to find the area of a rhombus given its diagonals. 2. **Formula for the area of a rhombus:** The area $A$ is given by $$A = \frac{d_1 \times d_2}{2}$$ where $d_1$ and $d_2$ are the lengths of the diagonals. 3. **Given values:** $$d_1 = 2 \text{ mm}, \quad d_2 = 4 \text{ mm}$$ 4. **Calculate the area:** $$A = \frac{2 \times 4}{2}$$ 5. **Simplify the expression:** $$A = \frac{\cancel{2} \times 4}{\cancel{2}} = 4 \text{ mm}^2$$ 6. **Final answer:** The area of the rhombus is $4$ square millimetres.