Expected outcomes two dice

I recently read the solution to the problem (#216 on mathproblems.info page) of expected number of rolls to roll every sum (2-12) at least once when rolling two dice. (61.2...). What I have been trying to work out since is the expected number of rolls for any combination of sums including the same sum multiple times. For example, what is the expected number of rolls to achieve the sum of 7 six times, the sum of 6 four times, and the sum of 8 four times. This leads to the question of what is the most efficient set (n) of sums. Suppose I wanted to get to a set of 14 numbers (as in the previous example) with the least number of rolls. What sums would I select and how many of each would I select? The current proposed solution for #216 does not seem to handle duplicate or greater sums.