There are 8 spaces between numbers, and each space has 2 choices. One * * * has two? =256 filling methods.

By trying (not necessarily to the end, some can be eliminated quickly), we can find an effective filling method for 12:

1+2+34-5+67-89= 10

12+3+45-67+8+9= 10

12+3-4-5-6-7+8+9= 10

12-3+4-5-6+7-8+9= 10

12-3-4+5+6-7-8+9= 10

123-45-67+8-9= 10

12-3-4+5-6+7+8-9= 10

12+3+4+5-6-7+8-9= 10

1-2-34-5+67-8-9= 10

12+3+4-5+6+7-8-9= 10

12-34+56-7-8-9= 10

1-2+34-5+6-7-8-9= 10