Evaluate sqrt(0.0625) - 12.4 / 0.4 x 3(1)/(8) of 2.56 + 8.68 without using a calculator.

The numerator is $\sqrt{0.0625} - 12.4 \div 0.4 \times 3$.
First, calculate the square root:

$$\sqrt{0.0625} = \sqrt{\frac{625}{10000}} = \frac{\sqrt{625}}{\sqrt{10000}} = \frac{25}{100} = 0.25$$

Next, perform the division:

$$12.4 \div 0.4 = \frac{12.4}{0.4} = \frac{124}{4} = 31$$

Then, perform the multiplication:

$$31 \times 3 = 93$$

Finally, perform the subtraction:

$$0.25 - 93 = -92.75$$

So, the numerator is $-92.75$.

The denominator is $\frac{1}{8} \text{ of } 2.56 + 8.68$.
First, calculate "$\frac{1}{8}$ of 2.56":

$$\frac{1}{8} \times 2.56 = \frac{2.56}{8}$$

To divide 2.56 by 8:

$$2.56 \div 8 = 0.32$$

Next, perform the addition:

$$0.32 + 8.68 = 9.00$$

So, the denominator is 9.

$$\frac{-92.75}{9}$$

To perform this division:

$$-92.75 \div 9 = -10.30555...$$

This is a repeating decimal. We can write it as $-10.30\overline{5}$.
Alternatively, as a fraction:

$$-\frac{92.75}{9} = -\frac{9275}{900}$$

Divide both numerator and denominator by 25:

$$-\frac{9275 \div 25}{900 \div 25} = -\frac{371}{36}$$

As a mixed number:

$$-\left(10 \frac{11}{36}\right)$$

The value of the expression is:

$$\boxed{-10.30\overline{5}} \quad \text{or} \quad \boxed{-\frac{371}{36}}$$