So first thankfully we own a wide assortment of dice including the mighty twenty sided ones and small tetrahedrons that we added to the game to speed it up. I had to allow any operations to be used that you wanted in order to accelerate the issue.
Then I had him think about the only roll that would allow him to get to 144 (4 sixes). Even one five and you'd be closer to 11^2. That provided a quick transition to calculating the probability 1/1296. As I told him, I'm not playing this for that long.