The total surface area of a cone is given by the formula \(A = \pi r^2 + \pi r l\), where A is the total surface area, r is the radius of the base, and l is the slant height of the cone. In this case, we are given that the radius of the cone is 2\(\sqrt{3}\)cm and the slant height is 4\(\sqrt{3}\)cm. Substituting these values into the formula, we get:

\[A = \pi (2\sqrt{3})^2 + \pi (2\sqrt{3})(4\sqrt{3})\]
\[= 12\pi + 24\pi\]
\[= 36\pi\]

So the total surface area of the cone is **36\(\pi \)cm²