Solution:

(i) As per the question,

$X=\{1,2,3\}$ in which $n$ represents any member of $X$

$\begin{array}{l}
X=\{1,2,3\} \\
\{4 n \mid n \in x\} \\
=\{4 \times 1,4 \times 2,4 \times 3\} \\
=\{4,8,12\}
\end{array}$

(ii) As per the question,

$X=\{1,2,3\}$ in which $n$ represents any member of $X$

$\begin{array}{l}
X=\{1,2,3\} \\
\{n+6 \mid n \in x\} \\
=\{1+6,2+6,3+6\} \\
=\{7,8,9\}
\end{array}$