To find the length of \(BC\), we use the sine rule:

\(\frac{AB}{\sin ACB} = \frac{BC}{\sin BAC}\)

Substitute the known values:

\(\frac{12}{\sin 45°} = \frac{x}{\sin 60°}\)

We know:

\(\sin 60° = \frac{\sqrt{3}}{2}\) and \(\sin 45° = \frac{1}{\sqrt{2}}\).

Substitute these into the equation:

\(\frac{12}{\frac{1}{\sqrt{2}}} = \frac{x}{\frac{\sqrt{3}}{2}}\)

Cross-multiply to solve for \(x\):

\(12 \times \frac{\sqrt{3}}{2} = x \times \frac{1}{\sqrt{2}}\)

\(12 \times \frac{\sqrt{3}}{2} \times \sqrt{2} = x\)

\(x = 6\sqrt{6}\)

Thus, the exact length of \(BC\) is \(6\sqrt{6}\).