Explanation

(a) When particle is at$x = 2$, the displacement is $y = 4\sim 2 = 2$ cm. If $r$ is the time taken by the particle to go from $x = 4$ cm to $x = 2$ cm, then
$y = a\cos{\omega t} = a\cos\frac{2\pi t}{T} = a\cos\frac{2\pi t}{1.2}$
or $\cos{\frac{2\pi t}{1.2} = \frac{y}{a}} = \frac{2}{4} = \frac{1}{2} = \cos\frac{\pi}{3}$
or $\frac{2t}{1.2} = \frac{1}{3}$ or $t = \frac{1.2}{6} = 0.26$
time taken to move from $x = + 2$ cm to $x = + 4$ cm and back again
$= 2t = 2 \times 0.2\ s = 0.4\ s$