Number of arrangements of the letters abcd in which neither ab nor cd come together.

Take AB as one unit and CD as one unit.
These can be arranged 2! factorial ways. Internally each can be arranged in 2!
Total ways 2x2x2=8 -(1)
Now count AB as once unit. Total ways of arranging is . 3!2 =12 -(2)
Similary count CD as one unit. Total ways of arranging is 3!x2=12 -(3)
Total ways for AB or CD together= 2+3- =16
Total ways for AB or CD not together = 4!-16=8