When I met him (1)/ the couple of days back (2)/ he was writing a new book. (3)/No error (4)

Answer

2

Explanation

a couple of days will replace the couple of days a couple of (something) : a few.
Look at the examples given below:
We went there a couple of years ago.
There are a couple of more files to read.
Hence, a couple of days back is the right usage