Włożyłem nowy głośnik do dużej kieszeni kurtki.

• włożyć is perfective: it describes a one-time, completed action (“to put in/insert” with focus on the result).
• wkładać is imperfective: it describes an ongoing, habitual or repeated action.
• Because the sentence refers to a single, completed event (“I put the speaker in”), we use the perfective past włożyłem.

• In Polish past tense, verbs agree in gender with the speaker.
• -łem is the ending for a masculine speaker (first person singular).
• A female speaker would say włożyłam (ending -łam).

• głośnik (“speaker”) is an inanimate masculine noun.
• In the accusative singular, inanimate masculine nouns have the same form as the nominative.
• If it were animate (e.g. student), the accusative would match the genitive (studenta).

• do expresses motion into something (the action of placing inside).
• do always governs the genitive case.
• The genitive singular of kieszeń is kieszeni (“into the pocket”).

• duża is the base (nominative feminine) form.
• After do, kieszeń is in genitive feminine, so the adjective must also be in genitive feminine.
• The genitive feminine ending for adjectives is -ej, hence dużej.

• kieszeni kurtki means “the pocket of the jacket.”
• In Polish, possession or “of”-relationships between nouns are expressed with the second noun in genitive.
• So kurtka → genitive singular kurtki.

• With verbs of motion or insertion like włożyć, Polish normally uses do + genitive to mark direction into.
• Using w + locative (w + dużej kieszeni) would sound odd here and might imply location rather than the act of placing.
• If you want to describe the final location without emphasizing the movement, you could say głośnik jest w dużej kieszeni kurtki (the speaker is in the pocket).

• The direct object “new speaker” can be replaced by the accusative pronoun go (masculine inanimate).
• The sentence becomes:
Włożyłem go do dużej kieszeni kurtki.