According to the given question,

\[{{t}_{1}}~=\text{ }2\text{ }and\text{ }{{t}_{3}}~=\text{ }8\]

General term is

\[{{t}_{n}}~=\text{ }a{{r}^{n\text{ }-\text{ }1}}\]

So,

\[{{t}_{1}}~=\text{ }a{{r}^{1\text{ }-\text{ }1}}~=\text{ }a\text{ }=\text{ }2\text{ }\ldots .\text{ }\left( 1 \right)\]

And,

\[{{t}_{3}}~=\text{ }a{{r}^{3\text{ }-\text{ }1}}~=\text{ }a{{r}^{2}}~=\text{ }8\text{ }\ldots .\text{ }\left( 2 \right)\]

Dividing (2) by (1), we get

\[a{{r}^{2}}/\text{ }a\text{ }=\text{ }8/\text{ }2\]

\[{{r}^{2}}~=\text{ }4\]

\[r\text{ }=\text{ }\pm \text{ }2\]

So, the \[~{{2}^{nd}}\]term of G.P. is

When \[a\text{ }=\text{ }2\text{ }and\text{ }r\text{ }=\text{ }2~\]is \[2\left( 2 \right)\text{ }=\text{ }4\]

Or when \[a\text{ }=\text{ }2\text{ }and\text{ }r\text{ }=\text{ }-2\] is \[2\left( -2 \right)\text{ }=\text{ }-4\]