$\displaystyle 2^k > 4k$

$\displaystyle 2^k > 4k = 2^k - 4k < 0$

$\displaystyle 2^{k+1}-4(k+1) = 2 x 2^k -4(k+1)$

$\displaystyle > 2 x 4k - 4(k+1)$, using $\displaystyle 2^k > 4^k,$

$\displaystyle =8k -4k - 4 = 4k -4$

I don't understand what has happened in the second to last step here.