To add these mixed numbers, we first need to convert them into improper fractions:

4 5/13 = (413 + 5)/13 = 53/13
8 7/15 = (815 + 7)/15 = 127/15
11 8/13 = (1113 + 8)/13 = 151/13
14 8/8 = (148 + 8)/8 = 120/8 = 15

Now, add the improper fractions:

53/13 + 127/15 + 151/13 + 15 = (5315 + 12713 + 15115 + 15195) / (13*15) = (795 + 1651 + 2265 + 195) / 195 = 4906/195

Now simplify the fraction:

4906/195 = 98/3

Therefore, 4 5/13 + 8 7/15 + 11 8/13 + 14 8/8 = 98/3 or 32 2/3.