Explanation

(b)
$The\ general\ termof\ \left( x + \frac{2}{x^{2}} \right)^{n}is$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\ T}_{R + 1} = \ ^{n}C_{R}(x)^{n - R}\left( \frac{2}{x^{2}} \right)^{R}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ ^{n}C_{R}x^{n - 3R}2^{R}$
For $x^{2r}$ occurs, it means
${\ \ \ \ \ \ \ \ \ \ \ \ \ n - 3R = 2r
}{\Longrightarrow \ \ \ \ \ \ \ n - 2r = 3R}$
Hence, $n - 2r$ is of the form $3k$