She is his great grandniece.
Your mother's brother is you uncle and your daughter's great uncle. Your daughter is his great niece.
Your nephew's daughter is your great niece and you are her great Aunt (or Great Uncle).Correction:Your nephew's daughter is your grand niece. You are her grand aunt or grand uncle.
You are the great aunt/uncle of your sister's son's daughter, and your sister's son's daughter is your great niece.
Your brother's daughter is your niece. Her daughter would be your great-niece. You would be either her great uncle or great aunt.
Your daughter is your uncle's grand niece.
Your grandmother's brother is your great uncle. Your great uncle's grandchildren are your second cousins.
If you are a woman, you are great great aunt to your niece's granddaughter. If you are a man, you are great great uncle to your niece's granddaughter. In either case, your niece's granddaughter is your great great niece.
Since your uncle's sister is your aunt, her daughter would be your cousin, just as your uncle's daughter would be.
Your sister's son's daughter is your sister's granddaughter and your great niece. (Some would say "grand niece.") You are her great uncle or great aunt.
Your sister's daughter is your niece. Your sister's granddaughter is your great niece Your sister's granddaughter's daughter (your sister's great granddaughter) is your great great niece. You are her great great aunt, if you are a woman, or her great great uncle, if you are a man.
You grandson is great great nephew to your uncle. You uncle is great great uncle to your grandson
You grandson is great great nephew to your uncle. You uncle is great great uncle to your grandson