$4\frac{5}{7} - (x - 6\frac{3}{7}) = 2\frac{6}{7}$
$4\frac{5}{7} - x + 6\frac{3}{7} = 2\frac{6}{7}$
$-x = 2\frac{6}{7} - 6\frac{3}{7} - 4\frac{5}{7}$
$x = 6\frac{3}{7} + 4\frac{5}{7} - 2\frac{6}{7}$
$x = (6 + 4 - 2) + (\frac{3}{7} + 4\frac{5}{7} - 2\frac{6}{7})$
$x = 8\frac{2}{7}$

$19\frac{28}{34} - (m + 2\frac{29}{34}) = 12\frac{15}{34}$
$-(m + 2\frac{29}{34}) = 12\frac{15}{34} - 19\frac{28}{34}$
$m + 2\frac{29}{34} = 19\frac{28}{34} - 12\frac{15}{34}$
$m = 7\frac{13}{34} - 2\frac{29}{34}$
$m = 6\frac{47}{34} - 2\frac{29}{34}$
$m = 4\frac{18}{34}$