Not all moves get scored. There may be a key move that gives you a certain success, in your example 66%, and you have to complete the puzzle for 100%
So, had the player not used the hint at all and failed the last two moves, it may still have given 66%. I can't say that is exactly what happened in the case you saw but I believe that is the way it works.
Here is what happened in my case.
Bob (let's say) is rated 1400 tactics and encountered a really hard problem that lasted 3 moves. He uses a hint for the 1st move and figures out the 2nd move. Then, he makes a mistake on the 3rd move. He gets 66% and an increase in rating, even though he only got 1 move right and 2 moves wrong. For some reason, the hint is not considered if he got less than 100%.
George does the same problem. He uses a hint on the 1st move and then proceeds to get the next 2 moves right. The message on the top says "Solved with hint", and he loses rating points, even though he got 2 moves right and 1 move wrong (which would be the first one).
If you try it right now, you can find that out. On one tactic, use a hint and then solve the rest. On a second tactic, use a hint and fail the 2nd move on purpose. The result will be better than the first time.
I rarely use hints (except after trying 3 or 4 times unsuccessfully -- just being blind sometimes). I have accidentally hit the hint button on the app in the past before the initial move and always lost points on those problems. I haven't had that happen in a while though.
So, I guess it is possible they have changed the process but as far as I know, using a hint at any point in the problem, will give you the same success/points as if you had missed that move and all subsequent moves.
In the new tactics trainer, chess players can use a "hint" so that the computer tells them what is the right move. The player can then choose to solve the rest of the problem. If they solve it, "Solved with Hint" will appear and it will score as if they got the problem incorrect with 0%. I don't use the hint often, but one day I found a problem.
This problem is, if one didn't finish the problem with 100% correct, it will give that person the percentage of moves he did get correct, including the one which he used a hint, For example, in a 3-move problem, if someone used a hint on the 1st move and then failed the 3rd move, they would get 66%. Their rating would also increase, while if they solved it completely right, their rating would decrease.
This means that anyone can get better than they would have by using a hint and failing what they think is the last move on purpose. Rating isn't the most important thing, but it still feels weird that you can do better by getting 40% or something than 100% if you used a hint. I would appreciate it if chess.com fixed this.