I am supposed to do corrections for this question but I do not know how.

The correct answer is $\displaystyle p = 2$

Here are the steps I have done:

$\displaystyle \lg(4^p - 4) - p\lg2 = \lg3$

$\displaystyle \lg(4^p - 4) - \lg2^p = \lg3

$

$\displaystyle \lg\frac{4^p - 4}{2^p} = \lg3$

$\displaystyle \frac{4^p - 4}{2^p} = 3$

$\displaystyle 4^p - 4 = 2^p \times 3$

$\displaystyle \frac{2^{2p} - 4}{2^p} = 3$

$\displaystyle \frac{2^{2p}}{2^p} - \frac{4}{2^p} = 3$

$\displaystyle 2^p - 2^{2 - p} = 3$

$\displaystyle 2^p(1 - 2^{2 - 1}) = 3$

Mr F says: This line is wrong. Expand it out to see why. $\displaystyle 2^p 2^{1} \neq 2^{2-p}$.
$\displaystyle 2^p = -3$

Any help would really be appreciated, thank you very much in advance!