Beitzah, chapter two, mishnah 6. This mishnah lists three matters in which Rabban Gamliel was stringent in accordance with the view of Beis Shammai. Although he was counted among the sages of Beis Hillel, in these three matters he followed Beis Shammai and not Beis Hillel.
The three matters in which Rabban Gamliel was stringent like Beis Shammai:
"Ein tomnin es ha'chamin mi'yom tov le'Shabbos" - one may not insulate hot food on Yom Tov for Shabbos. At the beginning of the chapter we learned about eiruv tavshilin, which permits cooking on Yom Tov for the sake of Shabbos, since by rabbinic law it is forbidden to cook on Yom Tov for Shabbos. According to Beis Shammai, here too one may make an eiruv tavshilin for the purpose of insulating food, but the eiruv itself must include insulating: one who wishes to bake needs bread in his eiruv; one who wishes to cook needs a cooked dish in his eiruv; and one who wishes to insulate must insulate something on the eve of Yom Tov. Every activity that he intends to do on Yom Tov for the sake of Shabbos, he must begin part of it before Yom Tov, as part of the eiruv tavshilin.
"Ve'ein zokfin es ha'menorah be'yom tov" - the plain meaning of "zokfin" is standing something upright, but the intention here is assembling the lamp: a candelabrum made of separate parts, which can be taken apart and reassembled. One may not assemble it on Yom Tov, because this looks like building. Beis Hillel disagree and hold that there is no prohibition of building with regard to vessels.
"Ve'ein ofin pitin gritzin ela rekikin" - one may not bake "pitin gritzin" on Yom Tov, which are very large loaves, but only "rekikin," thin wafers. The difference lies in the amount of effort involved: preparing the large loaves is a far more complicated and exhausting process than preparing the wafers, and therefore according to Beis Shammai they are not permitted, and Rabban Gamliel was stringent in this.
Rabban Gamliel's words and the sages' reply:
Rabban Gamliel gave a reason for his practice: "Mi'yamai lo hayu ofin beis abba pitin gritzin ela rekikin" - in his father's house they never baked the large loaves, only wafers, and therefore he too conducts himself this way.
The sages answered him: "Mah na'aseh le'veis avicha, she'hayu machmirin al atzman u'mekilin le'chol Yisrael" - it is true that the members of his father's household were stringent upon themselves to bake only the thin wafers, whose preparation is easy, and not the thick, large loaves; but toward the rest of Israel they were lenient, "she'yihyu ofin pitin gritzin ve'chori" - they permitted them to bake large loaves, and even "chori," which are apparently loaves that are larger still.
In other words, his father's household's practice of stringency was merely a personal stringency, not a halachic ruling; in the way they ruled the halachah for all of Israel, they were lenient in this matter. Therefore what Rabban Gamliel saw in his own home is no proof of what the halachah truly is.
In summary: this mishnah listed three matters in which Rabban Gamliel followed Beis Shammai - insulating hot food on Yom Tov for Shabbos, assembling the lamp on Yom Tov, and baking pitin gritzin - and we learned the sages' reply to his reasoning, that his father's household's practice was a stringency upon themselves alone, while for all of Israel they were lenient.