I assume that the word “string” refers to a fixed arrangement of letters which must be preserved as a group. If this is the case then the letters of the string cannot be permutated－the letters must be preserved in the order they are given. The string is a fixed single quantity.
(a) The string DE is isolated from the other letters and treated as a single quantity. The remaining 6 letters constitute 6 quantities making 7 in all, which generate 7!=5040 perms.
(b) CDE is isolated and treated as a fixed quantity. The remaining letters constitute 5 quantities, making 6 quantities with 6!=720 perms.
(c) AB and FGH are two distinct quantities. The remaining 3 letters constitute 3 more quantities, making 5 in all, for which there are 5=120 perms.
(d) The three given strings constitute 3 distinct quantities. The remaining two letters make up 5 quantities, so there are 5!=120 perms in total.
(e) CAB, BED make up one quantity only: CABED which preserves the two individual strings. 3 letters remain, making 4 quantities in all, with 4!=24 perms.
(f) BCA and ABF cannot be arranged so as to preserve each string. So there are no possible permutations.