The first digit is 2

That leaves digits 1,2,3,3,4,6,6,6

The first two digits then are 21, 22, 23, 24, or 26

If the first two digits are 21, the last digit is either 2,3,4, or 6
If the first two digits are 22, the last digit is either 1,3,4, or 6
If the first two digits are 23, the last digit is either 1,2,3,4, or 6
If the first two digits are 24, the last digit is either 1,2,3, or 6
If the first two digits are 26, the last digit is either 1,2,3,4, or 6

I count 22.

That's not too many, so I'll just list them:

 1. 212
 2. 213
 3. 214
 4. 216
 5. 221
 6. 223
 7. 224
 8. 226
 9. 231
10. 232
11. 233
12. 234
13. 236
14. 241
15. 242
16. 243
17. 246
18. 261
19. 262
20. 263
21. 264
22. 266

Edwin