Answer
$\phi = \frac{\pi}{2}$
Work Step by Step
It is given in the question that $y(0,0) = 4.0~cm$
$y(x,t) = (y_m) ~sin(kx \pm \omega t + \phi)$
$y(0,0) = (4.0~cm) ~sin(0 \pm 0 + \phi) = 4.0~cm$
$(4.0~cm) ~sin(\phi) = 4.0~cm$
$sin(\phi) = 1$
$\phi = \frac{\pi}{2}$
