All of the sentences you provided contain both a noun phrase and a verb phrase. However, if you want to identify specifically, here is a brief analysis:
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"Some dog breeds have docked tails."
- Noun phrase: "Some dog breeds"
- Verb phrase: "have docked tails"
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"You can find frogs and insects by the pond if you look closely enough."
- Noun phrases: "You", "frogs and insects", "the pond"
- Verb phrases: "can find", "look closely enough"
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"He sat on my grandmother's favorite armchair."
- Noun phrase: "He", "my grandmother's favorite armchair"
- Verb phrase: "sat on"
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"The pigeons have not landed on my neighbor's balcony in a long time."
- Noun phrase: "The pigeons", "my neighbor's balcony"
- Verb phrase: "have not landed on"
In summary, each of the sentences contains both a noun phrase and a verb phrase, but if you need to pick only one, any of them would work.