An atom of hydrogen has a radius of about 0.1 nm.

Step 1. The width of one atom. $2 \times 0.1\ \text{nm} = 0.2\ \text{nm}$.

Step 2. The line in nanometres. $3\ \text{mm} = 3 \times 10^{6}\ \text{nm}$.

Step 3. The number of atoms. $\dfrac{3 \times 10^{6}\ \text{nm}}{0.2\ \text{nm}} = 1.5 \times 10^{7}$.