To determine the number of chairs made in 21 days, we need to calculate the combined productivity of all three carpenters and then multiply it by the number of days.

First, let`s find the productivity of each carpenter. Carpenter A can make a chair in 6 hours, so in one hour, they can make 1/6th of a chair. Similarly, carpenter B can make 1/7th of a chair in one hour, and carpenter C can make 1/8th of a chair in one hour.

To calculate the combined productivity, we need to add up the individual productivities of the three carpenters:

Combined productivity per hour = 1/6 + 1/7 + 1/8

To add these fractions, we need a common denominator. The least common multiple of 6, 7, and 8 is 168, so let`s convert the fractions to have a denominator of 168:

Combined productivity per hour = (28/168) + (24/168) + (21/168)

= 73/168

Now, we know the combined productivity of the three carpenters in one hour is 73/168 of a chair.

Since each carpenter works for 8 hours per day, their combined productivity in one day will be:

Combined productivity per day = (73/168) * 8

= 73/21

Now, we can calculate the number of chairs made in 21 days by multiplying the combined productivity per day by the number of days:

Number of chairs made in 21 days = (73/21) * 21

= 73

Therefore, the correct answer is Option 3: 73. According to the calculations, the carpenters will make a total of 73 chairs in 21 days.