If A is non-singular square matrix of order 3 and |A^-1|=24, then the…

$|A^{-1}|=24$ so $\frac{1}{|A|}=24$ so $|A|=\frac{1}{24}$

$|3A|=\frac{3^3}{24}=\frac{9}{8}$

so $|2A||adj(3A)|=2^3|A||3A|^2$

$=2^3×\frac{1}{24}×\frac{9}{8}×\frac{9}{8}$

$=\frac{27}{64}$