To find the set of values of \(k\) for which the line \(l\) does not intersect the curve, substitute \(y = k - 2x\) from the line equation into the curve equation \(xy = 12\).

This gives:

\(x(k - 2x) = 12\)

\(kx - 2x^2 = 12\)

Rearrange to form a quadratic equation:

\(2x^2 - kx + 12 = 0\)

For the line not to intersect the curve, the quadratic equation must have no real roots. This occurs when the discriminant \(b^2 - 4ac < 0\).

Here, \(a = 2\), \(b = -k\), and \(c = 12\).

Calculate the discriminant:

\((-k)^2 - 4(2)(12) < 0\)

\(k^2 - 96 < 0\)

Thus, \(k^2 < 96\).

Taking the square root of both sides gives:

\(-\sqrt{96} < k < \sqrt{96}\)

Therefore, the set of values of \(k\) for which the line does not intersect the curve is \(|k| < \sqrt{96}\).