G3.4 $P$ is a point located at the origin of the coordinate plane. When a dice is thrown and the number $n$ shown is even, $P$ moves to the right by $n$. If $n$ is odd, $P$ moves upward by $n$. Find the value of $d$, the total number of tossing sequences for $P$ to move to the point $(4,4)$.
Possible combinations of the die:
$2,2,1,1,1,1$. There are ${ }_{6} C_{2}$ permutations, i.e. 15 .
$4,1,1,1,1$. There are ${ }_{5} C_{1}$ permutations, i.e. 5 .
$2,2,1,3$. There are ${ }_{4} C_{2} \times 2$ permutations, i.e. 12 .
$4,1,3$. There are 3 ! permutations, i.e. 6 .
Total number of possible ways $=15+5+12+6=38$.