The figure shows the graph of a function $y = f(x)$ on the interval $[-2, 4]$. It is made of three straight pieces joining the points $(-2, 2)$, $(0, -2)$, $(2, 2)$ and $(4, -2)$, and $f$ is defined only on this interval. How many solutions in $[-2, 4]$ does the equation $f(f(x)) = 0$ have?

Fig. 1: The graph of y = f(x) on the interval from x = -2 to x = 4: three straight pieces joining the points (-2, 2), (0, -2), (2, 2) and (4, -2), forming a zigzag. The axes are marked from -2 to 4 on the x-axis and from -2 to 2 on the y-axis, with a light grid.