This is taken from The Fellowship of the Ring, book II, chapter 1, page 266:
If he had the cheek to make verses about Eärendil in the house of Elrond, it was my affair.
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Aragorn uses “cheek” here with the meaning “impertinence” or “mild disrespect”. Bilbo has just recited a poem about the mythical figure Eärendil, in verse that is playful in metre and vocabulary, and at times rather fanciful (for example, it’s doubtful that Eärendil’s scabbard was made of chalcedony). But we learn shortly that Eärendil was Elrond’s father:
‘So it was indeed,’ answered Elrond gravely. ‘But my memory reaches back even to the Elder Days. Eärendil was my sire, who was born in Gondolin before its fall; and my mother was Elwing, daughter of Dior, son of Lúthien of Doriath. I have seen three ages in the West of the world, and many defeats, and many fruitless victories.’
J. R. R. Tolkien (1954). The Fellowship of the Ring, book II, chapter 2. London: Allen & Unwin.
Aragorn is right that it is a little bit impertinent for a guest to recite poetry about his host’s father.