Graph the system of inequalities. Then find the coordinates of the vertices.
\[
\begin{array}{l}
y \geq-4 \\
x \geq 6
\end{array}
\]

Step 1 ：The problem is asking to graph the system of inequalities and find the coordinates of the vertices. The system of inequalities consists of two inequalities: \(y \geq -4\) and \(x \geq 6\).

Step 2 ：The first inequality, \(y \geq -4\), is a horizontal line that passes through the point (0, -4) and includes all the points above it.

Step 3 ：The second inequality, \(x \geq 6\), is a vertical line that passes through the point (6, 0) and includes all the points to the right of it.

Step 4 ：The intersection of these two inequalities forms a region in the upper right quadrant of the coordinate plane. The vertices of this region are the points where the lines intersect the axes.

Step 5 ：To find the coordinates of the vertices, we need to find the points where the lines intersect the axes. The line \(y = -4\) intersects the y-axis at (0, -4) and the line \(x = 6\) intersects the x-axis at (6, 0).

Step 6 ：The vertices of the region defined by the system of inequalities are at the points \(\boxed{(0, -4)}\) and \(\boxed{(6, 0)}\).