A rope is tied to a post at its far end…

Step 1. The numbers. $k = \dfrac{2\pi}{1.6\ \text{m}} = 3.93\ \text{rad/m}$. $\omega = 2\pi \times 2.5\ \text{Hz} = 15.7\ \text{rad/s}$. $v = f\lambda = 2.5\ \text{Hz} \times 1.6\ \text{m} = 4\ \text{m/s}$.

Step 2. The direction. The wave moves towards $-x$, so the phase is $kx + \omega t$.

Step 3. The start. Try $y = a\sin(kx + \omega t)$. At $x = 0$ and $t = 0$, $y = a\sin 0 = 0$. A moment later $\omega t$ is a little positive, so $y$ is positive: the point moves up. Both conditions hold, so $\phi = 0$.