(i) To find the first three terms of \((2-x)^6\), we use the binomial expansion formula:

\((2-x)^6 = \sum_{k=0}^{6} \binom{6}{k} (2)^{6-k} (-x)^k\).

The first three terms are:

\(\binom{6}{0} (2)^6 (-x)^0 = 64\),

\(\binom{6}{1} (2)^5 (-x)^1 = -192x\),

\(\binom{6}{2} (2)^4 (-x)^2 = 240x^2\).

Thus, the first three terms are \(64 - 192x + 240x^2\).

(ii) We need the coefficient of \(x^2\) in \((1 + 2x + ax^2)(2-x)^6\).

From part (i), the expansion of \((2-x)^6\) gives us the terms \(64 - 192x + 240x^2\).

Consider the terms contributing to \(x^2\):

1. \(1 \cdot 240x^2 = 240x^2\)

2. \(2x \cdot (-192x) = -384x^2\)

3. \(ax^2 \cdot 64 = 64ax^2\)

The total coefficient of \(x^2\) is \(240 - 384 + 64a\).

Set this equal to 48:

\(240 - 384 + 64a = 48\)

\(64a = 192\)

\(a = 3\)