After Max was sent to her office at Spoonerville Jr. High School, Miss Pennypacker questioned him about his falling asleep in Mr. Hammerhead's class, dressing like a dipstick, eating like a goat, and allowing his lunch to drip onto the floor (which caused Mr. Hammerhead to slip and fall down). She reassured him that he wasn't in trouble, but expressed her concern that Max, being the child of a single parent, might be too much for his father, Goofy, to handle. Max tried to dissuade her worries by falsely claiming that his father was set to be getting married soon, which interested Miss Pennypacker into wanting to meet the bride-to-be.
Two days later, Miss Pennypacker walked to the Goofs' house in the evening to pay them a visit and check up on how Max and Goofy were getting along. However, thanks to an arrangement set up by Pete, she arrived just as Pete's street pavement worker Gilda (whom Pete tricked into coming over to Goofy's house for an estimate while Goofy mistook her for his date for that evening) was chasing after Pete in anger for his tricking her, after Goofy ended up accidentally wrecking his own living room with Gilda's jackhammer. Gilda and Pete ran right at Miss Pennypacker and sent her spinning like a spinning top. When she stopped spinning, the dizzy and disoriented Miss Pennypacker made her way up to the Goofs' front door. Upon entering the house, she was caught off guard by Goofy, who mistook her for Gilda and starting dancing with her with his eyes closed. Once she and Goofy came crashing to the ground, Miss Pennypacker finally regained her wits and Goofy realized his mistake.
Max and Peg, Pete's wife, attempted to explain the situation to Miss Pennypacker (as the living room had been ruined by the aforementioned jackhammer incident) and tried to reassure her that Goofy is a good father. But much to Max and Goofy's sadness, Miss Pennypacker remained concerned more than ever that all this confusion would make studying difficult for Max, and felt that he should stay somewhere else. Thus, Peg opted to allow Max to stay with her and her family until all of this could be sorted out.
The following night, she paid one more visit to the Goofs' house to check on Goofy and Max, where she witnessed Goofy giving Max everything he would need until he could get the house fixed. Among said items was Max's school report on Bigfoot that both Max and Miss Pennypacker thought Max had already turned in, but seeing how Goofy found the rest of it (on top of the previous tender moment of Goofy giving Max everything he'd need until the house was fixed) convinced Miss Pennypacker that she had jumped to the wrong conclusion about Goofy and Max the night before and apologized to the two of them. Though, she also felt, to be absolutely sure, that she and Goofy ought to discuss the matter further over dinner and dancing, which Goofy delightedly accepted. Max tagged along as well and the three of them walked hand in hand down the sidewalk together, with Goofy inquiring to Miss Pennypacker if she knew anything about fixing chimneys.
As Miss Pennypacker never appeared in any other episode (or in any other media outside of Goof Troop), and since Goofy appeared to remain single in all other episodes (and even got a different girlfriend in An Extremely Goofy Movie), it is presumable that any potential romantic relationship between Goofy and Miss Pennypacker ultimately did not come to fruition.