$81\times\left (\frac{16}{25} \right )^{x+2}\div\left (\frac{3}{5} \right )^{2x+4}=144$
$\implies9^{2}\times\left (\frac{16}{25} \right )^{x+2}\div\left (\frac{3}{5} \right )^{2x+4}=144$
$\implies9^{2}\times\left (\frac{4}{5} \right )^{2(x+2)}\div\left (\frac{3}{5} \right )^{2(x+2)}=12^{2}$
$\implies\left [ 9\times\left (\frac{4}{5} \right )^{x+2}\div\left (\frac{3}{5} \right )^{x+2}\right ]^{2}=12^{2}$
$\implies\left [ 9\times\left (\frac{4}{5} \right )^{x+2}\div\left (\frac{3}{5} \right )^{x+2}\right ]=12$
$\implies \left [\left (\frac{4}{5} \right )^{x+2}\div\left (\frac{3}{5} \right )^{x+2}\right ]=\frac{4}{3}$
$\implies\frac{\left(\frac{4}{5}\right)^{x+2}}{\left(\frac{3}{5}\right)^{x+2}} = \frac{4}{3}$
$\implies\left(\frac{4}{3}\right)^{x+2}= \left(\frac{4}{3}\right)^{1}$
Compare both side and we get
$x+2=1$
$\implies x=-1$
So, correct answer is option (B).