Which sentence is spelled correctly? a. they're going to the restaurant to pick up their order. b. they're going to the restaurant to pick up there order. c. they're going to the restaurant to pick up they're order. d. their going to the restaurant to pick up there order

Answer is A. They're going to the restaurant to pick up their order.

Their is used for possession.

"There order" is grammatically incorrect, as there is used for location.
"They're order" is grammatically incorrect, as they're is a contraction for "They are", and "They are order" is nonsense.
"Their going" is grammatically incorrect, as their is for possession.