Hello, Michelle! How are you?

I didn't find any interactions listed between the Penicillin and the Methadone, but there may be issues if you take the Mucinex D, since it contains Pseudoephedrine, which works like a stimulant and the Methadone is a depressant, so you should check with your doctor, before combining those.

Penicillin is an antibiotic and according to the FDA, it may cause side effects, such as nausea, dizziness, headache, non-allergic skin rash and diarrhea. [1]

Mucinex-D is listed as containing Guaifenesin and Pseudoephedrine, it is used to alleviate congestion. Typical side effects may include nausea, dizziness, insomnia and nervousness. [2], [3]

Methadone is list as being a narcotic analgesic, so it has the potential to be habit forming and may cause side effects, such as nausea, dizziness, drowsiness, dry mouth and constipation. [4]

I hope this helps!