(i) Express the general point of l in component form: \((1 + s, 1 - s, 1 + 2s)\).

Express the general point of m in component form: \((4 + 2t, 6 + 2t, 1 + t)\).

Equate the components:

\(1 + s = 4 + 2t\)

\(1 - s = 6 + 2t\)

\(1 + 2s = 1 + t\)

Solving these equations, we find \(s = -1\) or \(t = -2\).

Verify that all three component equations are satisfied with these values.

(ii) The direction vector of l is \((1, -1, 2)\) and of m is \((2, 2, 1)\).

Calculate the scalar product: \(1 \times 2 + (-1) \times 2 + 2 \times 1 = 2 - 2 + 2 = 2\).

Calculate the moduli: \(\sqrt{1^2 + (-1)^2 + 2^2} = \sqrt{6}\) and \(\sqrt{2^2 + 2^2 + 1^2} = \sqrt{9} = 3\).

Divide the scalar product by the product of the moduli: \(\frac{2}{\sqrt{6} \times 3}\).

Evaluate the inverse cosine: \(\cos^{-1}\left(\frac{2}{3\sqrt{6}}\right)\).

The acute angle between the lines is \(74.2^\circ\) (or 1.30 radians).