To solve the equation -4|5x| + 6 2/5 = -5.6, we first need to simplify the mixed number on the right side of the equation:

6 2/5 = 6 + 2/5 = 6 + 2/5 = 31/5

So the equation becomes:

-4|5x| + 31/5 = -5.6

Next, we isolate the absolute value term by moving the constant to the other side:

-4|5x| = -5.6 - 31/5

-4|5x| = -28/5

Now, we can divide by -4 to solve for |5x|:

|5x| = -28/5 / -4

|5x| = 28/20

|5x| = 7/5

Now, we solve for x by considering both the positive and negative cases of the absolute value:

5x = 7/5 or 5x = -7/5

x = 7/5 / 5 = 7/25 or x = -7/5 / 5 = -7/25

Therefore, the solutions to the equation are x = 7/25 and x = -7/25.