1.) To solve ||x-2|=5, we need to consider two cases:
i) x-2 = 5
ii) x-2 = -5

i) x-2 = 5
Adding 2 to both sides:
x = 7

ii) x-2 = -5
Adding 2 to both sides:
x = -3

Therefore, the solutions to ||x-2|=5 are x = 7 and x = -3.

2.) To solve ||2x-12|+4|=8, we again consider two cases:
i) 2x-12+4 = 8
ii) -(2x-12)+4 = 8

i) 2x-8 = 8
Adding 8 to both sides:
2x = 16
Dividing by 2:
x = 8

ii) -(2x-12)+4 = 8
-2x + 12 + 4 = 8
-2x + 16 = 8
Subtracting 16 from both sides:
-2x = -8
Dividing by -2:
x = 4

Therefore, the solutions to ||2x-12|+4|=8 are x = 8 and x = 4.