(i) To expand \((2x - x^2)^6\), use the binomial theorem:

\((a - b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} (-b)^k\)

Here, \(a = 2x\), \(b = x^2\), and \(n = 6\).

The first three terms are:

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

\(\binom{6}{1} (2x)^5 (x^2)^1 = -192x^7\)

\(\binom{6}{2} (2x)^4 (x^2)^2 = 240x^8\)

Thus, the first three terms are \(64x^6 - 192x^7 + 240x^8\).

(ii) To find the coefficient of \(x^8\) in \((2 + x)(2x - x^2)^6\), consider the terms that contribute to \(x^8\):

1. \((2)(240x^8) = 480x^8\)

2. \((x)(-192x^7) = -192x^8\)

The coefficient of \(x^8\) is \(480 - 192 = 288\).