A graphene sheet is a plane of hexagons…

Step 1. Area for each atom. The hexagon has an area of $\dfrac{3\sqrt{3}}{2}(141.5\ \text{pm})^2 = 5.202 \times 10^4\ \text{pm}^2$. Two atoms share it: $2.601 \times 10^4\ \text{pm}^2 = 2.601 \times 10^{-20}\ \text{m}^2$ each.

Step 2. Mass for each atom. $12.011 \times 10^{-3}\ \text{kg/mol} / (6.022 \times 10^{23}) = 1.9945 \times 10^{-26}\ \text{kg}$.

Step 3. Mass for each square metre. $1.9945 \times 10^{-26} / 2.601 \times 10^{-20} = 7.67 \times 10^{-7}\ \text{kg} = 0.767\ \text{mg}$.

Step 4. Area of one gram. $1.00\ \text{g} / 0.767\ \text{mg/m}^2 = 1304\ \text{m}^2$.

Step 5. Density of graphite. A column of $1\ \text{m}^2$ with a height of $335\ \text{pm}$ holds $0.767\ \text{mg}$. Volume: $3.35 \times 10^{-10}\ \text{m}^3$. Density: $7.67 \times 10^{-7}\ \text{kg} / 3.35 \times 10^{-10}\ \text{m}^3 = 2289\ \text{kg/m}^3 = 2.29\ \text{g/cm}^3$.