(i) Start with the equation:

\(3(2 \sin x - \cos x) = 2(\sin x - 3 \cos x)\)

Expand both sides:

\(6 \sin x - 3 \cos x = 2 \sin x - 6 \cos x\)

Rearrange to collect like terms:

\(6 \sin x - 2 \sin x = -6 \cos x + 3 \cos x\)

\(4 \sin x = -3 \cos x\)

Divide both sides by \(\cos x\):

\(\frac{4 \sin x}{\cos x} = -3\)

\(\tan x = -\frac{3}{4}\)

(ii) From \(\tan x = -\frac{3}{4}\), find the general solution:

\(x = \tan^{-1}\left(-\frac{3}{4}\right)\)

\(x \approx -36.9^\circ\)

Adjust for the range \(0^\circ \leq x \leq 360^\circ\):

\(x = 180^\circ - 36.9^\circ = 143.1^\circ\)

\(x = 360^\circ - 36.9^\circ = 323.1^\circ\)