A wave is represented by the equation y=0.2...

The given wave equation is $y = 0.2 \sin 4\pi \left[ \dfrac{t}{0.08} + \dfrac{x}{0.8} + \dfrac{1}{12} \right]$

Comparing this with the standard wave equation $y = A \sin(\omega t + kx + \phi)$

$\omega = \dfrac{4\pi}{0.08} = 50\pi$ rad/s

$k = \dfrac{4\pi}{0.8} = 5\pi$ rad/m

Since the signs of $\omega t$ and $kx$ are the same, the wave is traveling in the negative x-direction.

The velocity of the wave is $v = \dfrac{\omega}{k} = \dfrac{50\pi}{5\pi} = 10$ m/s

The wavelength is $\lambda = \dfrac{2\pi}{k} = \dfrac{2\pi}{5\pi} = 0.4$ m

Answer: negative x-direction with velocity 10 m/s and with wavelength 0.4 m.