The possible outcomes when a coin is tossed once is either a Head $\left( H \right)$ or a Tail $\left( T \right)$.
The possible outcomes when a die is thrown are $1,2,3,4,5$ and $6$.
Only when head is shown on the coin then only a die is rolled. So, the number of sample space $ = 1 \times 6$
$ = 6$
Thus, the sample space ${S_H} = \left\{ {H1,{\text{ }}H2,{\text{ }}H3,{\text{ }}H4,{\text{ }}H5,{\text{ }}H6} \right\}$.
Now, when tail is shown on the coin upon tossing, then the sample space ${S_T} = \left\{ T \right\}$.
Therefore, the sample space when a coin is tossed and then a die is rolled only in case a head is shown on the coin is
$S = \left\{ {H1,H2,H3,H4,H5,H6,T} \right\}$.