The spellings thank you and thank-you are both correct, but they have different uses.

thank you

Without a hyphen, thank you is a verb with a direct object. We use this phrase to show our gratitude to someone:

• Thank you, Alan, for the lovely lawn mower!
• I want to thank you, Ms. Krishna, for your valuable help.

thank-you

With a hyphen, thank-you is either a noun or an adjective. As a noun, it means “a message of thanks”:

• Mark sent Joan a thank-you for the lava lamp she gave him.

As an adjective, thank-you is used before a noun and means “expressing thanks”:

• I received a thank-you card from my stockbroker.