To identify $a$ and $b$ for the hyperbola given in the form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, you need to determine the vertices and slopes of the asymptotes.

1. Vertices: Look at where the hyperbola intersects the x-axis. In the graph, the hyperbola intersects at $(-4,0)$ and $(4,0)$, so: $a = 4$

2. Asymptotes: The asymptotes are the blue dashed lines. They appear to pass through $(0,0)$ with slopes that form a rectangle centered at the origin. From the grid, it looks like the slope is $\pm \frac{b}{a} = \pm \frac{6}{4} = \pm \frac{3}{2}$.

Using this relationship: $b = 6$

Therefore, $a = 4$ and $b = 6$.