Is it possible to model these probabilities in AnyDice?

I was asked by a pal to help him model a dice mechanic in AnyDice. I must admit I am an absolute neophyte with it, and I offered to solve it using software I’m better versed in. I’d like to be able to help them do this in AnyDice.

The mechanic is as follows:

  • The player and their opponent are each assigned a pool of dice. This is done via other mechanics of the game, of which details are not germane. Suffice to say, the player will have some set of dice (say 2D6, 1D8, and 1D12) that will face off against the opponents pool (which will generally be different from the player’s, say 3D6, 2D8 and 1D12).
  • The player and their oppoent roll their pools.
  • The opponent notes their highest value die. This is the target.
  • The player counts the number of their dice that have a higher value than the target, if any.
  • The count of the dice exceeding the target, if any, is the number of success points.

I searched the AnyDice tag here for questions that might be similar, the closest I found was "Modelling an opposed dice pool mechanic in AnyDice", specifically the answer by Ilmari Karonen.

That question and answer, however, deals with only a single die type.

Can a question like "What are the probabilities of N successes when rolling 4D6 and 6D20 as the player against 6D6 and 4D20 for the opponent?", be handled in AnyDice and produce a chart similar to that below?

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