$$5\frac{1}{4}+6\frac{2}{3}+7\frac{1}{6}=?$$

First, we convert mixed fractions into proper fractions:
$$5\frac{1}{4}=\frac{21}{4}$$
$$6\frac{2}{3}=\frac{20}{3}$$
$$7\frac{1}{6}=\frac{43}{6}$$
Now, $$5\frac{1}{4}+6\frac{2}{3}+7\frac{1}{6}=\frac{21}{4}+\frac{20}{3}+\frac{43}{6}$$

= $$\frac{229}{12}$$

In mixed fraction form 229/12 = $$19\frac{1}{12}$$
Option C is correct.