1) For the first equation, |4x+5|=5:
We have two cases to consider:
1) 4x + 5 = 5
4x + 5 - 5 = 5 - 5
4x = 0
x = 0

2) -(4x + 5) = 5
-4x - 5 = 5
-4x - 5 + 5 = 5 + 5
-4x = 10
x = -2.5

So the solutions for this equation are x = 0 and x = -2.5.

2) For the second equation, |x| + 8 = 6:
We have two cases to consider:
1) x + 8 = 6
x = 6 - 8
x = -2

2) -x + 8 = 6
-x = 6 - 8
-x = -2
x = 2

So the solutions for this equation are x = -2 and x = 2.

3) For the third equation, ||x|| = 10:
We have two cases to consider:
1) |x| = 10
This means x is either 10 or -10.

2) -|x| = 10
This has no real solutions as the absolute value of x cannot be negative.

So the solutions for this equation are x = 10 or x = -10.

Overall, the solutions to the given equations are:
1) x = 0 or x = -2.5
2) x = -2 or x = 4
3) x = 10 or x = -10