Loke ROJh said, in Florida 6/53 you can mark up to 5 of the 6 numbers on the playslip check the QP box and the terminal will randomly select the remaining numbers, but the will be from from all the remaining 49, not a set you provide.
The free lottery software that will do what you want is the Maybell Quik Wheeler, select game size to establish a grid with all the numbers. Right click on your 4 Key Numbers (any), left click on your other 6 (any). In this case I right clicked on 1-4 and left clicked on 5-10. Drawback, only full wheels.
1: 1-2-3-4-5-6
2: 1-2-3-4-5-7
3: 1-2-3-4-5-8
4: 1-2-3-4-5-9
5: 1-2-3-4-5-10
6: 1-2-3-4-6-7
7: 1-2-3-4-6-8
8: 1-2-3-4-6-9
9: 1-2-3-4-6-10
10: 1-2-3-4-7-8
11: 1-2-3-4-7-9
12: 1-2-3-4-7-10
13: 1-2-3-4-8-9
14: 1-2-3-4-8-10
15: 1-2-3-4-9-10
This 4+2 wheel you could have constructed by hand, simple progression, 3+3 would be harder.
If you don't want a full wheel and random selection of the other numbers, but you can't limit them to 6 and not a full wheel, you could try CoverMaster, set for . . .
Pick: 4 (first) Pool: 47 or (two below game size) Match 3 Hits 4: Enter your 4 key numbers on as many lines as you want to play. Raise one to two below game size Raise Pick to 5 it will ask if you want to pick a number or random, go with random, raise Pick to game size it will again ask for a pick or random. You will likely get more then 6 different numbers. Here I picked 12-13-14-15 as keys no control available over random.
12 13 14 15 36 42
12 13 14 15 24 36
12 13 14 15 43 44
12 13 14 15 31 41
12 13 14 15 43 48
5 7 12 13 14 15
1 12 13 14 15 32
1 12 13 14 15 39
12 13 14 15 26 44
12 13 14 15 30 36
10 12 13 14 15 24
12 13 14 15 19 29
12 13 14 15 28 46
12 13 14 15 25 32
12 13 14 15 29 43
Get it here: http://www.lotto-logix.com/wheellinks.html
BobP