Answer
$\phi = 1.9~rad$
Work Step by Step
$x = (6.0~cm)~cos(\omega~t+\phi)$
Note that when $t = 0$, then $x = -2.0~cm$
We can let $t = 0$ to find the phase constant $\phi$:
$x = (6.0~cm)~cos(\omega~t+\phi) = -2.0~cm$
$(6.0~cm)~cos(0+\phi) = -2.0~cm$
$cos(\phi) = -\frac{1}{3}$
$\phi = cos^{-1}~(-\frac{1}{3})$
$\phi = 1.9~rad$
