Explanation:

From the given conditions, for the four positions available :
1 cannot come at the first place. So 2, 3 and 4 can appear there.
4 cannot come at the last place. So 1, 2 and 3 can appear there.
2 and 3 cannot immediately follow each other. So 23 and 32 is not allowed.
1 cannot be immediately followed by 3. So 13 is not allowed.
Let us list the possible numbers now -
2431 --- possible, does not violate any condition
2143 --- possible, does not violate any condition
3142 --- possible, does not violate any condition
3412 --- possible, does not violate any condition
3421 --- possible, does not violate any condition
4312 --- possible, does not violate any condition
Hence, answer is (a). Total 6 numbers are possible.