Answer
The probability is $\frac{1}{6}$.
Work Step by Step
We know that there are six outcomes, so $\text{n}\left( \text{S} \right)=\text{ 6}$.
There are two outcomes in the green stopping event, so $\text{n}{{\left( \text{E} \right)}_{\text{green}}}=\text{ 2}$.
And the probability of stopping on red is given below,
$\text{P}{{\left( \text{E} \right)}_{\text{green}}}\text{ = }\frac{\text{n}{{\left( \text{E} \right)}_{\text{green}}}}{\text{n}\left( \text{S} \right)}\text{ = }\frac{2}{6}\text{ }$
And the event of stopping on a number less than 4 can be represented by
${{\left( \text{E} \right)}_{\text{less than 4}}}\text{ }=\text{ }\left\{ 1,2,3 \right\}$
There are three outcomes in this event, so $\text{n}{{\left( \text{E} \right)}_{\text{less than 4}}}=\text{ 3}$.
And the probability of stopping on less than $4$ is given below
$\text{P}{{\left( \text{E} \right)}_{\text{less than 4}}}\text{ = }\frac{\text{n}{{\left( \text{E} \right)}_{\text{less than 4}}}}{\text{n}\left( \text{S} \right)}\text{ = }\frac{3}{6}\text{ }$
Thus, the probability of stopping on green on first spin and a number less than $4$ on second spin is
$\begin{align}
& \text{P}\left( \text{red on first spin and less than 4 on second spin} \right)=\text{P}\left( \text{red} \right)\times \text{P}\left( \text{less than 4} \right) \\
& =\frac{2}{6}\times \frac{3}{6} \\
& =\frac{6}{36} \\
& =\frac{1}{6}
\end{align}$
