The answer is false.
The formula for the SA of a cone is [tex] \pi r^{2}+\pi rl[/tex] where r is the radius of the base and l is the slant height.
Since we have both the slant's height and the radius of the base we can answer this just by plugging numbers in;
[tex]SA=\pi r^{2}+\pi rl\\
SA=\pi (2^{2})+\pi (2)(6)\\
SA=4\pi+12\pi\\
SA=16\pi\\[/tex]
[tex]16\pi[/tex]≈50.2654...
So your answer is false.
