To solve \(|x - 2| = \left|\frac{1}{3}x\right|\), consider the cases for the absolute values.

Case 1: \(x - 2 = \frac{1}{3}x\)

Rearrange to get: \(x - \frac{1}{3}x = 2\)

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

\(x = 3\)

Case 2: \(x - 2 = -\frac{1}{3}x\)

Rearrange to get: \(x + \frac{1}{3}x = 2\)

\(\frac{4}{3}x = 2\)

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

Thus, the solutions are \(x = 3\) or \(x = \frac{3}{2}\).