For this question, I found the answer as $n= 2$ Let me explain How I got that: Let $X$ represents the number that comes up on the die.
Therefore the game continues as long as $X<6$,
So, $P(X=6)=nCrp^r q^{n−r}$ where $r=1$ then we have $\dfrac{1}{6}=nC_1 \times \dfrac{1}{6} \times \biggr (\dfrac{5}{6}\biggr )^{n-1}$ Which gives $ n = 1$
