Conditional formatting comparing values across different tables

Yes, you are on the right track and basically there.

I think the main issue is that because you have text in your BonusGoals[Goal] column, it can't be recognized as a number column to compare against number of encounters. I would either remove that row or make the goal null, and change format to number, although the below measure should work with your data as is (IFERROR + VALUE are handling the text):

GoalMet = 
CALCULATE(
    VAR CurGoal = IFERROR(VALUE(SELECTEDVALUE(BonusGoals[Goal])),BLANK()) RETURN
    IF([Encounters]>= CurGoal && ISNUMBER(CurGoal),1,0),
    Services
)

P.S. as Greg_Deckler also mentions, your NumberHours measure can just be DISTINCTCOUNT(Services[Encounter ID])  -- no need for the calculate or filtering, since the dates and encounter IDs are in the same table so relationship between encouters and dates are implicitly known.