can I mix Banner Max or mancozeb with Eagle20
Absolutely yes! I do this with both propiconazole and Myclobutanil and it is very effective at black spot control.
Clarification, Eagle and Honor Guard are in the same MOA category so you would not mix them together. You would combine either or with Mancozeb. Eagle has been researched to do very well with black spot control besides being very effective on Powdery mildew.
Banner Maxx (aka Honor Guard) and Eagle have the same mode of action (MOA). There is no point in mixing them. Alternate them with Compass or its less expensive generic alternative called Flint for best results.
The question was can I mix eagle20 with Banner Max or Mancozeb
Please do not mix Banner Maxx and Eagle together, they are the same type of systemic chemical. You should mix either of them with Mancozeb which is a contact fungicide.