會同館 The Hall Of Assembly
不多時，轉過隅頭，忽見一座門牆，上有「會同館」三字。唐僧道：「徒弟，我們進這衙門去也。」行者道：「進去怎的？」不多时，转过隅头，忽见一座门墙，上有「会同馆」三字。唐僧道：「徒弟，我们进这衙门去也。」行者道：「进去怎的？」
逐句解 Line by line
Before long they turned a corner and came suddenly upon a gated wall, and above it stood three characters: Hall of Common Assembly.
隅頭 is a street corner. The three characters over this gate answer the three on the city banner a few passages back — the second sign in the chapter that has to be read, and this time nobody argues about it.
The Tang Monk said, "Disciples, let us go into this office."
衙門 is a government office, and this is its only appearance in the chapter. Calling the place by that word rather than by its name is what makes the errand sound official before any reason has been given for going in.
Pilgrim said, "Go in for what?"
怎的 is everyday speech for 'what for'. Four characters, and the shortest reply in the passage.
A 會同館 was a real institution — the office where a court received foreign envoys and lodged travelling officials, something between an embassy and a government guest house. Tripitaka heads for it without being directed, which tells us he knows the procedure of these kingdoms by now.
Pilgrim's question is impatience rather than obstruction. He has no business at such a place and cannot see why they should stop — and the answer he gets is the first time in the chapter that his master explains something to him instead of being corrected.