What is the propositional phrase preposition and object in the following

1. I hung the valuable painting in the library.
2. The eggs inside the nest are not to be distributed.

http://www.chompchomp.com/terms.htm

Read about prepositions and prepositional phrases here. Then let us know what you decide.

I think for number 1 the

Phrase: the
Preposition: valuable painting in the library
Object: valuable painting

I think you need to go back into your text and that website and read those explanations and examples again! Study them. Study = memorize!

Examples:
He played for the Boston Red Sox.
preposition = for
object of preposition = Boston Red Sox
prepositional phrase = for the Boston Red Sox

She wanted to dance in the ballet.
preposition = in
object of preposition = ballet
prepositional phrase = in the ballet

Here are some further websites for you to study:
https://www.englishclub.com/grammar/prepositions.htm
and
http://grammar.ccc.commnet.edu/grammar/prepositions.htm
+
http://grammar.ccc.commnet.edu/grammar/phrases.htm#preposition

Thank you for the sites

But I'm still confused

In the given sentences, the prepositional phrase, preposition, and object can be identified as follows:

1. Sentence: "I hung the valuable painting in the library."
Prepositional phrase: "in the library"
Preposition: "in"
Object: "the library"

Explanation:
To identify the prepositional phrase, we need to look for a preposition and its associated object. In this sentence, the preposition "in" introduces the prepositional phrase "in the library." And the object of the preposition is "the library."

2. Sentence: "The eggs inside the nest are not to be distributed."
Prepositional phrase: "inside the nest"
Preposition: "inside"
Object: "the nest"

Explanation:
Similar to the first sentence, we can identify the prepositional phrase by locating the preposition and its object. In this sentence, the preposition "inside" introduces the prepositional phrase "inside the nest," and the object of the preposition is "the nest."