To identify which sentence contains both a noun phrase and a verb phrase, let's analyze each option:
a. "some dog breeds have docked tails" - Noun phrase: "some dog breeds"; Verb phrase: "have docked tails"
b. "he sat on my grandmother's favorite armchair" - Noun phrase: "my grandmother's favorite armchair"; Verb phrase: "sat"
c. "the pigeons have not landed on my neighbor's balcony in a long time" - Noun phrase: "the pigeons"; Verb phrase: "have not landed"
d. "you can find frogs and insects by the pond if you look closely enough" - Noun phrases: "frogs and insects" and "the pond"; Verb phrases: "can find" and "look"
All four sentences contain both noun phrases and verb phrases. However, if we need to choose just one option that includes both elements, any of the above is valid.
So, the answer is: All options (a, b, c, and d) contain both noun phrases and verb phrases.