The surface area of a cylinder is

Where r = 6cm and h = 12cm.
![\begin{gathered} S=2\pi\cdot6\operatorname{cm}\cdot12\operatorname{cm}+2\pi(6\operatorname{cm})^2 \\ S=452.16(cm)^2+226.08(cm)^2 \\ S=678.24(cm)^2 \end{gathered}]()
Therefore, the surface area is 678.24 square centimeters.
The lateral surface area would be

Because is the first term of the surface area formula.
Therefore, the lateral surface area is 452.16 square centimeters.