Euler says:

$v-e+f = 2$

If one tries to tessellate the sphere surface with solely hexagon. Let $x$ be the number of hexagon, then:

\begin{align} v &= 6x/3 \\ e &= 6x/2 \\ f &= x \\ v - e + f &= 2x-3x+x = 2 \end{align}

To make tessellation possible, we have to add $y$ pentagons, so that:
\begin{align} v &= (6x+5y)/3 \\ e &= (6x+5y)/2 \\ f & = x+y \\ v-e+f &= y/6 = 2 \end{align}
So we can solve and get $y = 12$.