First, let's convert the mixed numbers to improper fractions:

12 3/4 = 51/4
3 9/4 = 21/4
4 - 1/4 = 15/4

Now, we can multiply the two fractions:
(51/4) * (21/4) = 1071/16

Finally, we can divide the result by 15/4:
(1071/16) / (15/4) = (1071/16) * (4/15) = 28584/240 = 1191/10

Therefore, 12 3/4 * 3 9/4 divided by 4 - 1/4 is equal to 1191/10.