Question

the study of an organism that lived 10 million years ago would most likely fall under which two branches of natural science?

Answer 1

paleontology and biology.

Answer 2

Paleontology means "the branch of science concerned with fossil animals and plants" (Merrium Webster Dictionary)
Biology is "a branch of knowledge that deals with living organisms and vital processes" (Merrium Webster)
Both of those natural science branches would investigate and study that organism. Good job!