a) To simplify the expression 5/12 - 7/22, we need to find a common denominator. The least common multiple of 12 and 22 is 132.

Converting the fractions to have a denominator of 132:
5/12 = (5/12) * (11/11) = 55/132
7/22 = (7/22) * (6/6) = 42/132

Now we can subtract the fractions:
55/132 - 42/132 = (55 - 42)/132 = 13/132

Therefore, 5/12 - 7/22 simplifies to 13/132.

b) To simplify the expression 46.54 - 2.6 x 3.12, we need to perform the multiplication first.

2.6 x 3.12 = 8.112

Now we can subtract:
46.54 - 8.112 = 38.428

Therefore, 46.54 - 2.6 x 3.12 simplifies to 38.428.

c) To solve the equation (24 x 15 - 2x) / (1/4) = 400, we need to isolate the variable x.

First, simplify the left side of the equation:
(24 x 15 - 2x) / (1/4) = 400
(360 - 2x) / (1/4) = 400
(360 - 2x) * 4 = 400

Now, solve for x:
1440 - 8x = 400
-8x = 400 - 1440
-8x = -1040
x = -1040 / -8
x = 130

Therefore, the value of x that satisfies the equation is 130.

d) To solve the equation 3200 / (8 + 3x) = 4, we need to isolate the variable x.

First, simplify the left side of the equation:
3200 / (8 + 3x) = 4

Now, cross-multiply:
3200 = 4(8 + 3x)
3200 = 32 + 12x

Next, solve for x:
3200 - 32 = 12x
3168 = 12x
x = 3168 / 12
x = 264

Therefore, the value of x that satisfies the equation is 264.