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I'll teach you fishing next Sunday.
Literal
Next-week [possessive-の] Sunday [on-に] fishing [object-を] teach-give-[volitional-よう].
~てあげる ('do X for [someone]') marks a giving-of-action benefit — the speaker is performing a favor. ~よう is the casual volitional 'I'll/let me.' Together: 'let me teach you fishing.' Note the ~てあげる can sound condescending if overused; here it's friendly between equals.