There multiple solutions and this is just one of them.

0 = 4+4-4-4.

1 = 44/44.

2 = 4+4-(4!/4).

3 = (4+4+4)/4.

4 = 4!-(4*4)-4.

5 = (4!/4)-(4/4).

6 = (4!/4)+4-4.

7 = (44/4)-4.

8 = 4+4+4-4.

9 = 4+4+4/4.

10 = (44-4)/4.