Rolls until a six given every roll is even

You keep rolling a fair die until a $6$ comes up, counting the final roll. Conditional on every roll in the sequence having been even, what is the expected number of rolls?

$\tfrac32$. Stop the process at the first roll that is not a 2 or 4; this time $T$ is geometric with success probability $\tfrac46$, and it is independent of which of 1, 3, 5, 6 ends it. The condition says that ending value is 6, which does not change the law of $T$, so the answer is $\mathbb{E}[T]=\tfrac{6}{4}=\tfrac32$.