To solve the first equation:

3 5/6 + a - 2 1/6 = 58 6/13
Convert all mixed fractions to improper fractions:
23/6 + a - 13/6 = 473/13
Combine like terms:
23/6 - 13/6 + a = 473/13
10/6 + a = 473/13
Simplify 10/6 to 5/3:
5/3 + a = 473/13
To isolate 'a' on one side, subtract 5/3 from both sides:
a = 473/13 - 5/3
a = 3644/39

So, a = 3644/39

To solve the second equation:

58 6/13 - (b + 9/13) = 4 2/13
Convert all mixed fractions to improper fractions:
760/13 - (b + 9/13) = 54/13
Distribute the negative sign:
760/13 - b - 9/13 = 54/13
Combine like terms:
(760 - 9)/13 - b = 54/13
751/13 - b = 54/13
To isolate 'b' on one side, subtract 751/13 from both sides:
-b = 54/13 - 751/13
-b = -697/13
Multiply both sides by -1 to solve for 'b':
b = 697/13

So, b = 697/13