$T(k)$ is the smallest number of steps needed to move from $k$ to $100$.
Now, it is given that $y$ and $z$ are two numbers such that,
$T(9) = 1 + min (T(y), T(z))$ , i.e.,
$T(9) = 1 + min ($Steps from $y$ to $100$, Steps from $z$ to $100)$, where $y$ and $z$ are two possible values that can be reached from $9$.
One number that can be reached from $9$ is $10$, which is the number obtained if we simply move one position right on the number line. Another number is $15$, the shortcut path from $9$, as given in the question. So, we have two paths from $9$, one is $10$ and the other is $15$.
Therefore, the value of $y$ and $z$ is $10$ and $15$ (either variable may take either of the values).
Thus, $yz = 150$.