Answer:
The correct pronoun to fill in the blank is:
From the first time they met, Walter and he never did get along well.
Step-by-step explanation:
Both "him" and "he" can be used, but it will depend on whether or not we need a subject. Suppose we did not need a subject here. Then it would be okay to use "him": "I remember when I first met Walter and him."
However, that is not the case with the sentence we are completing in this exercise. "Walter" and "he" are both the subject of "never did get along". One way to test that out is by separating the subjects:
Walter never got along. OK
Him never got along. NOT OK
He never got along. OK
Thus, the sentence should be:
From the first time they met, Walter and he never did get along well.