To solve this problem, we need to find a common denominator for all the fractions involved.

First, let's find a common denominator for 12, 16, 24, and 4² which is 48.

Then, we convert all fractions to have a denominator of 48:

(28/48) - (9/48) - (10/48) + (1/16)

Now we can combine the fractions:

(28 - 9 - 10) / 48 + 1/16
= 9 / 48 + 1/16
= 3/16 + 3/16
= 6/16
= 3/8

Therefore, (7/12 - 3/16 - 5/24) + (1/4²) equals 3/8.