Identify the proposition and the object of the preposition in sentence near the wooded island, two otters played contentedly

The preposition here is the word near. Just like its Latin name says it, a preposition means a word that stands before a noun, signifying its relation to something else. The object of the preposition here is the wooded island. It is a noun or a noun phrase that immediately follows the preposition. In this sentence, the island is related to the otters in that they are placed near it.

preposition: near; object of the preposition: island

Near the wooded island is a prepositional phrase - - begins with a preposition (near) and ends with an object (island). The is an article adjective and wooded is an adjective.