To determine which point satisfies both inequalities, let's analyze each inequality separately and then check the given points:

1. $y < -x - 4$
2. $y > \frac{5}{4}x + 1$

First, we will substitute each point into both inequalities to see if they satisfy the conditions.

Point (1, -8)

1. $y < -x - 4$ $-8 < -1 - 4$ $-8 < -5$ (True)
2. $y > \frac{5}{4}x + 1$ $-8 > \frac{5}{4}(1) + 1$ $-8 > 1.25 + 1$ $-8 > 2.25$ (False)

Point (6, 5)

1. $y < -x - 4$ $5 < -6 - 4$ $5 < -10$ (False)
2. $y > \frac{5}{4}x + 1$ $5 > \frac{5}{4}(6) + 1$ $5 > 7.5 + 1$ $5 > 8.5$ (False)

Point (-6, -3)

1. $y < -x - 4$ $-3 < 6 - 4$ $-3 < 2$ (True)
2. $y > \frac{5}{4}x + 1$ $-3 > \frac{5}{4}(-6) + 1$ $-3 > -7.5 + 1$ $-3 > -6.5$ (True)

Point (-2, 3)

1. $y < -x - 4$ $3 < 2 - 4$ $3 < -2$ (False)
2. $y > \frac{5}{4}x + 1$ $3 > \frac{5}{4}(-2) + 1$ $3 > -2.5 + 1$ $3 > -1.5$ (True)

Based on this analysis, the point that satisfies both inequalities is:

$\boxed{(-6, -3)}$

Would you like further details or have any questions? Here are 5 additional questions you might find useful:

1. How do you solve systems of linear equations?
2. What are the properties of linear inequalities?
3. Can you explain how to graph inequalities on a coordinate plane?
4. How do you determine the feasible region for a system of inequalities?
5. What is the difference between strict and non-strict inequalities?

Tip: When graphing inequalities, always start by graphing the boundary line, then use a test point to determine where to shade.