Yahweh hardened Pharaoh's heart

Here "heart" refers to Pharaoh. His stubborn attitude is spoken of as if his heart was hard. See how you translated this phrase in Exodus 9:12. Alternate translation: "caused Pharaoh to became more defiant" (See: rc://en/ta/man/jit/figs-synecdoche and rc://en/ta/man/jit/figs-metaphor)

he would not let them go

"Pharaoh would not let them go"