The equation of a waves  $y=4\sin \left\{\frac{\pi }{2}(2t+\frac{x}{8})\right\}$ is where y, x are in cm and time in seconds. The amplitude , wavelength, velocity and frequency of the wave are, respectively

Comparing the given equation with general wave equation ;

$\mathrm{y}=\mathrm{Asin}(\mathrm{\omega t}-\mathrm{kx})$

Here, 

$\mathrm{A}=4\mathrm{cm}$

$\mathrm{\omega }=\mathrm{\pi rad}/\mathrm{s}$

$\Rightarrow \mathrm{Frequency} \mathrm{f}=\frac{\mathrm{\omega }}{2\mathrm{\pi }}=0.5s^{-1}$

$\mathrm{k}=\frac{\mathrm{\pi }}{16}$

$\Rightarrow \mathrm{\lambda }=\frac{2\mathrm{\pi }}{\mathrm{k}}=32\mathrm{cm}$

Velocity of the wave is 

$\mathrm{V}=\mathrm{f\lambda }=32\times 0.5=16\mathrm{cm}/\mathrm{s}$