Let us assume that there are 8 people organised in 4 couples (say AaBbCcDd). Each person is to give a gift to each other (individually) over the course of 6 rounds such that:
Each person cannot get himself or his significant other (i.e. each person has 6 potential people they can give a gift to)
Each person gifts once and only once to each potential person they can gift to within the 6 rounds
Two members of one couple cannot get two members of another couple (in any round, at any point)
Here is an example solution I came up with in my head (I can only somewhat see the pattern):
i.e. in round 1 A gives to B, a to C, B to c, C to D, c to A, D to a and d to b...
How many other alternatives exist? What are they?
First guess upper bound:
(6*4)^4 * (5*4)^4 * (4*2)^4 * (3*2)^4 * (2*1)^4 * (1*1)^4 = 4508684868648960000
A lot
There is definitely no way to list them all. A trivial lower limit would be 6!=720 (permuting the rows of the solution you already found) which is still too many to list here.
Second guess:
Just realised the above upper bound allows for one person receiving multiple gifts in a round. So the real answer must be significantly less.