She hung a small Picasso painting on the living room wall.

Literal

She [topic-は] living-room [attributive-の] wall [on-に] small Picasso [attributive-の] painting [object-を] hung.

Note the two の particles doing different attributive work: 居間の壁 ('the living room's wall' — location relation) and ピカソの絵 ('Picasso's painting' — authorship). Both are the same particle, but the relationship it expresses depends entirely on the nouns it joins. The form 小さな is unusual: it functions as an attributive ('small') only, and unlike the regular 小さい cannot stand as a predicate (×絵が小さなだ). A handful of words behave this way — 大きな, 小さな, おかしな — sometimes called 連体詞 ('attributive-only words'). 居間 is the older, more native term for living room (literally 'the staying room'), still common in contrast to the imported リビング. Pablo Picasso (1881–1973) is widely known in Japan; major works are held by museums in Tokyo and Hakone, and his name is often the first to come up in any reference to modern Western painting.