A wave travels along a rope. Graph (a) shows the whole rope at t = 0…

Step 1. Read the graphs. The amplitude is $5\ \text{cm}$. Graph (a) repeats every $0.8\ \text{m}$, so $\lambda = 0.8\ \text{m}$. Graph (b) repeats every $0.08\ \text{s}$, so $T = 0.08\ \text{s}$.

Step 2. Speed. $v = \dfrac{\lambda}{T} = \dfrac{0.8\ \text{m}}{0.08\ \text{s}} = 10\ \text{m/s}$.

Step 3. Direction. Graph (b) shows that the point at $x = 0$ moves down first. In graph (a) the rope to the right of $x = 0$ is above the axis, and the rope to the left would be below it. The point at $x = 0$ takes the shape of the rope that arrives next. It goes down, so the rope arriving next comes from the left. The wave travels towards $+x$. As a check, $y = 5\sin(kx - \omega t)$ fits both graphs: at $t = 0$ it is $5\sin kx$, and at $x = 0$ it is $-5\sin\omega t$.

Step 4. Phase difference. $\Delta\phi = \dfrac{2\pi}{\lambda}\Delta x = \dfrac{2\pi}{0.8\ \text{m}} \times 0.15\ \text{m} = 1.18\ \text{rad}$, which is $67.5^\circ$.