7.
Since each spin can be considered an independent event and that there's only 4 possible outcomes for each event, we can trivially, enumerate all 16 possible combinations and examine them to see if they meet the desired criteria. So:
11, 13, 14, 16, 31, 33, 34, 36, 41, 43, 44, 46, 61, 63, 64, 66
Let's prune the above list to just those with a sum greater than 5.
16, 33, 34, 36, 43, 44, 46, 61, 63, 64, 66
Now prune the above list to just those with an odd number.
16, 33, 34, 36, 43, 61, 63
And finally, count them to determine that there's 7 possible outcomes.
