Calculate the values of the following expressions, using reciprocals from tables where necessary.

The reciprocal of 807 is $\frac{1}{807}$.

$$\frac{1}{807} \approx 0.001239157$$

The reciprocal of 0.0541 is $\frac{1}{0.0541}$.

$$\frac{1}{0.0541} \approx 18.48428835$$

$$\frac{2}{807} + \frac{4}{0.0541} = 2 \times \frac{1}{807} + 4 \times \frac{1}{0.0541}$$

Substitute the reciprocal values:

$$2 \times 0.001239157 + 4 \times 18.48428835$$ $$0.002478314 + 73.9371534$$ $$73.939631714$$

Rounding to four decimal places:

$$\boxed{\text{73.9396}}$$

The expression is $\frac{1}{3} \left( \frac{2}{0.6638} + \frac{3}{0.833} \right)$.
This can be written as:

$$\frac{1}{3} \left( 2 \times \frac{1}{0.6638} + 3 \times \frac{1}{0.833} \right)$$

(These values would typically be looked up in reciprocal tables.)

$$\frac{1}{0.6638} \approx 1.506478$$ $$\frac{1}{0.833} \approx 1.200480$$

$$\frac{1}{3} (2 \times 1.506478 + 3 \times 1.200480)$$ $$\frac{1}{3} (3.012956 + 3.60144)$$ $$\frac{1}{3} (6.614396)$$ $$2.20479866...$$

Rounding to four decimal places:

$$\boxed{\text{2.2048}}$$

The numerator is $12.76625 - 12.4 + 0.3 \times 3$.
First, calculate the multiplication:

$$0.3 \times 3 = 0.9$$

Next, perform the subtraction:

$$12.76625 - 12.4 = 0.36625$$

Finally, perform the addition:

$$0.36625 + 0.9 = 1.26625$$

So, the numerator is 1.26625.

The denominator is $\frac{1}{8} \text{ of } 2.56 + 3.68$.
First, calculate $\frac{1}{8} \text{ of } 2.56$:

$$\frac{1}{8} \times 2.56 = \frac{2.56}{8} = 0.32$$

Next, perform the addition:

$$0.32 + 3.68 = 4.00$$

So, the denominator is 4.00.

$$\frac{1.26625}{4}$$ $$1.26625 \div 4 = 0.3165625$$ $$\boxed{\text{0.3165625}}$$