The riddle
If Teresa's Daughter Is My Daughter's Mother, What Am I to Teresa?
Step by step
Start in the middle. "My daughter's mother" is the woman who gave birth to the speaker's daughter. For a woman speaking, that woman is herself. So the sentence says that Teresa's daughter is the speaker, which makes the speaker Teresa's daughter. The riddle is a long way of saying "I am my mother's daughter", and it fits in one breath once that is clear.
If the speaker is a man
A man who tells the riddle has a different answer. His daughter's mother is usually his wife, so Teresa's daughter is his wife, and he is Teresa's son-in-law. Both answers are common: "daughter" as the intended answer, and "son-in-law" for a male speaker.
Why it feels so hard
Three family words are packed into one sentence: daughter, mother and daughter again. Each one seems to point to a new person, and the answer comes from noticing that two of those phrases land on the same woman. Readers lose the thread by treating "Teresa's daughter" and "my daughter's mother" as two different women, when they are one.
Drawing it out
Write Teresa at the top, then draw a line down to her daughter. Next draw a line from that daughter down to a child. The speaker is the mother of that child, so the speaker is the box in the middle. Marking which box is the speaker turns a puzzle that looks impossible into a three-box diagram: Teresa, her daughter, and the child. Doing it on paper takes half a minute.