$\log_6144-\log_64 = \log_612^2-\log_64 = 2\log_612 -\log_64$ 

 $2\log_612 -\log_64 = 2\log_6(3 *4) -\log_64 = 2(\log_63 + \log_64) -\log_64$ 

 $2\log_63 + 2\log_64 -\log_64 = 2\log_63 + \log_64$ 

$\displaystyle { 2 \left( \frac{\log_3 3}{\log_3 6} \right) + \log_64 = \frac{2 \log_3 3}{\log_3 6} + \frac{ \log_3 4}{\log_3 6} = \frac{ {\log_3 3^2} + \log_3 4}{\log_3 6} }$ 

 $\displaystyle { \frac{ {\log_3 9 \cdot 4} }{\log_3 6} = \frac{ {\log_3 36} }{\log_3 6} = \frac{ {\log_3 6^2} }{\log_3 6} = \frac{ {2 \log_3 6 } }{\log_3 6} = 2 }$