To solve these equations, we will go step by step:

1) x - 7 = 5
To isolate x, we add 7 to both sides:
x - 7 + 7 = 5 + 7
x = 12

2) 128 - 3 x [ x + 4 ] = 23
First, we simplify the expression inside the brackets:
128 - 3 x (x + 4) = 23
128 - 3x - 12 = 23
Combine like terms:
128 - 12 - 3x = 23
116 - 3x = 23
To isolate x, we subtract 116 from both sides:
116 - 116 - 3x = 23 - 116
-3x = -93
Divide both sides by -3:
-3x / -3 = -93 / -3
x = 31

3) [[ 6x - 39 ] : 7 ] x 4 = 12
First, we simplify the expression inside the brackets:
[6x - 39] / 7 x 4 = 12
[6x - 39] / 7 = 12 / 4
[6x - 39] / 7 = 3
To isolate the expression inside the brackets, we multiply both sides by 7:
[6x - 39] / 7 x 7 = 3 x 7
6x - 39 = 21
To isolate x, we add 39 to both sides:
6x - 39 + 39 = 21 + 39
6x = 60
Divide both sides by 6:
6x / 6 = 60 / 6
x = 10

4) [ x : 3 - 4 ] x 5 = 15
First, we simplify the expression inside the brackets:
[x/3 - 4] x 5 = 15
To isolate the expression inside the brackets, we divide both sides by 5:
[x/3 - 4] x 5 / 5 = 15 / 5
x/3 - 4 = 3
To isolate x, we add 4 to both sides:
x/3 - 4 + 4 = 3 + 4
x/3 = 7
Multiply both sides by 3:
(x/3) x 3 = 7 x 3
x = 21

5) [ 3x - 2^4 ] x 7^3 = 2 x 7^4
First, we simplify the exponents:
[3x - 16] x 343 = 2 x 2401
To isolate the expression inside the brackets, we divide both sides by 343:
[3x - 16] x 343 / 343 = 2 x 2401 / 343
3x - 16 = 2 x 7
3x - 16 = 14
To isolate x, we add 16 to both sides:
3x - 16 + 16 = 14 + 16
3x = 30
Divide both sides by 3:
3x / 3 = 30 / 3
x = 10

6) x - [ 42 + [ - 28 ]] = - 8
First, we simplify the expression inside the inner brackets:
x - [42 + (-28)] = -8
x - [42 - 28] = -8
x - 14 = -8
To isolate x, we add 14 to both sides:
x - 14 + 14 = -8 + 14
x = 6

Therefore, the solutions to the equations are:
x = 12, 31, 10, 21, 10, 6.