Раскроем скобки: $$19\frac{28}{34} - m - 2\frac{29}{34} = 12\frac{15}{34}$$.
$$19\frac{28}{34} - 2\frac{29}{34} - m = 12\frac{15}{34}$$.
$$16\frac{33}{34} - m = 12\frac{15}{34}$$.
$$m = 16\frac{33}{34} - 12\frac{15}{34} = 4\frac{18}{34} = 4\frac{9}{17}$$
Ответ: $$m = 4\frac{9}{17}$$