Step 1:
$8y^2-2x^2=16$
The above equation is divided by $16$ we get
$\large\frac{y^2}{2}-\frac{x^2}{8}$$=1$
$\Rightarrow a^2=2,b^2=8$
$\Rightarrow a=\sqrt 2,b=2\sqrt 2$
Step 2:
Transverse axes : $y$-axes (i.e) $x=0$
Conjugate axes : $x$-axes (i.e) $y=0$
Length of transverse axis,$2a=2\sqrt 2$
Length of conjugate axis,$2b=2\times 2\sqrt 2=4\sqrt 2$