A body in SHM has an amplitude of 4 cm and a frequency of 2 Hz…

Step 1. $\omega$. $\omega = 2\pi f = 2\pi \times 2\ \text{Hz} = 4\pi\ \text{rad/s} = 12.6\ \text{rad/s}$.

Step 2. Two choices. $4\ \text{cm} \times \cos\phi = 2\ \text{cm}$, so $\cos\phi = 0.5$. Then $\phi = \pi/3$ or $\phi = -\pi/3$.

Step 3. Pick by the direction. At $t = 0$, $v = -A\omega\sin\phi$. The body moves towards the mean position, that is towards $-x$, so $v < 0$. That needs $\sin\phi > 0$, so $\phi = \pi/3 = 1.05\ \text{rad}$.

Step 4. Equation. $x = 4\cos(4\pi t + \pi/3)$, with $x$ in cm.

Step 5. At 0.25 s. The phase is $4\pi\ \text{rad/s} \times 0.25\ \text{s} + \pi/3 = \pi + \pi/3$. So $x = 4\ \text{cm} \times \cos(4\pi/3) = -2\ \text{cm}$.