The first step is to make everything improper fractions:
So 12 3/4 becomes 51/4 and 5 1/3 becomes 16/3
To add 51/4 and 16/3, both denominators need to be the same, so we can multiply by a factor of 1 to get both denominators to equal 12 as shown:
51/4*3/3=153/12
16/3*4/4=64/12
Now you can just add 153/12+64/12 to get 217/12, which in mixed number form is 18 1/12
So 12 3/4 + 5 1/3 is 18 1/12