Assume that $1,2,3,4,5$ and $6$ are the possible outcomes when the die is thrown.

When a coin is tossed then the possible outcomes can be either Head $(H)$ or Tail $(T).$

Consider,

Case 1: Head is encountered

Sample space ${{S}_{1~}}=\text{ }\left\{ HT,\text{ }HH \right\}$

Case 2: Tail is encountered

Sample Space ${{S}_{2~}}=\text{ }\left\{ \left( T,1 \right),\text{ }\left( T,2 \right),\text{ }\left( T,3 \right),\text{ }\left( T,4 \right),\text{ }\left( T,5 \right),\text{ }\left( T,6 \right) \right\}$

Therefore, the Sample space of the event is

$S\text{ }=\text{ }\left\{ \left( HT \right),\text{ }\left( HH \right),\text{ }\left( T1 \right),\text{ }\left( T2 \right),\text{ }\left( T3 \right),\text{ }\left( T4 \right),\text{ }\left( T5 \right),\text{ }\left( T6 \right) \right\}$