지갑을 집에 두고 왔어. I left my wallet at home. 지갑을 집에 놔두고 왔어. This has almost the same meaning as above. Honestly, I don't know the difference between these two. 두고 is from the verb 두다. 놔두고 is from the verb 놔두다, which is a shortened form of 놓아두다. You can guess that 놓아 in 놓아두다 might be from the verb 놓다, and it really has that kind of meaning 놓다; but 놓아두다 is just one different word. So you don't write 놓아 and 두다 separately. 지갑을 집에 놓고 왔어. is also possible and commonly used.

놔 is shortened word of 놓아.. 놓아 means put down.. 놔두다 is 'let something be'