Solve the following expression: 6 rac78 + 8 rac12 imes 6 rac12

$$6\frac{7}{8} = \frac{6 \times 8 + 7}{8} = \frac{48 + 7}{8} = \frac{55}{8}$$ $$8\frac{1}{2} = \frac{8 \times 2 + 1}{2} = \frac{16 + 1}{2} = \frac{17}{2}$$ $$6\frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2}$$

The expression becomes:

$$\frac{55}{8} + \frac{17}{2} \times \frac{13}{2}$$

$$\frac{17}{2} \times \frac{13}{2} = \frac{17 \times 13}{2 \times 2} = \frac{221}{4}$$

The expression is now:

$$\frac{55}{8} + \frac{221}{4}$$

To do this, find a common denominator, which is 8.
Convert $\frac{221}{4}$ to an equivalent fraction with a denominator of 8:

$$\frac{221}{4} = \frac{221 \times 2}{4 \times 2} = \frac{442}{8}$$

Now add the fractions:

$$\frac{55}{8} + \frac{442}{8} = \frac{55 + 442}{8} = \frac{497}{8}$$

Divide 497 by 8:

$$497 \div 8 = 62 \text{ with a remainder of } 1$$

So, the mixed number is $62\frac{1}{8}$.

The final answer is \boxed{\text{62\frac{1}{8}}}.