|2/3 x – 4| = 10

To solve the equation (|frac{2}{3}x – 4| = 10), we need to consider the two cases that arise from the absolute value.

1. Case 1: (frac{2}{3}x – 4 = 10)

Adding 4 to both sides:

(frac{2}{3}x = 14)

Now, multiply both sides by (frac{3}{2}):

(x = 21)

2. Case 2: (frac{2}{3}x – 4 = -10)

Adding 4 to both sides:

(frac{2}{3}x = -6)

Now, multiply both sides by (frac{3}{2}):

(x = -9)

Putting both solutions together, we find (x = -9) and (x = 21).

The correct answer is C. {-9, 21}.