To solve this problem, we need to determine how many 3/4-yard sections can be made from the total length of the 6 boards.

Step 1: Find the total length of the boards

Each board is $\frac{7}{8}$ yards long, and there are 6 boards.

$\text{Total length} = 6 \times \frac{7}{8} = \frac{42}{8} = 5.25 \text{ yards}$

Step 2: Determine how many 3/4-yard sections can be made

Next, we divide the total length of the boards by the length of each section (3/4 yards):

$\text{Number of sections} = \frac{5.25}{\frac{3}{4}} = 5.25 \times \frac{4}{3} = \frac{21}{4} = 5.25 \times 1.33 = 7 \text{ sections}$

Therefore, the carpenter can construct 7 sections of 3/4-yard length from the 6 boards.

Would you like more details, or do you have any questions? Here are some related questions:

1. How would the answer change if the boards were 1 yard each?
2. How many 1-yard sections can be made from the same total length?
3. What is the leftover length of wood after making the 7 sections?
4. How many 1/2-yard sections could be made instead?
5. What if the boards were 5/8 yards long instead?

Tip: When dividing fractions, remember that dividing by a fraction is the same as multiplying by its reciprocal.