A capsule is a cylinder with a hemisphere on each end…

Step 1. The radius. $r = 3\ \text{mm}$.

Step 2. The cylinder part. $h = 18\ \text{mm} - 2 \times 3\ \text{mm} = 12\ \text{mm}$.

Step 3. The cylinder. $2\pi r h = 2\pi \times 3\ \text{mm} \times 12\ \text{mm} = 72\pi\ \text{mm}^2$.

Step 4. The two ends. $4\pi r^2 = 4\pi \times (3\ \text{mm})^2 = 36\pi\ \text{mm}^2$.

Step 5. The total. $72\pi + 36\pi = 108\pi\ \text{mm}^2$, which is $339.3\ \text{mm}^2$.