We know that, Average = Sum of all observations/Number of observations

According to the given information,

Average of 7 numbers is 21

? The average of first and sixth numbers is 19

first number + sixth number = 19 × 2 = 38

And, since Average of the third, fifth and seventh numbers is $(24\frac{1}{3})$

∴ third number + fifth number + seventh number $(= \;24\frac{1}{3}\; \times 3\; = \;73)$

Now, since the second number is less than the fourth number by 8, let the second number be x thus, fourth number would be x + 8.

Thus,

21 = (sum of all seven numbers)/7

$(\Rightarrow \frac{{x\; + \;x\; + \;8\; + \;73\; + \;38\;}}{7} = 21)$

⇒ 2x + 119 = 147

⇒ 2x = 28

⇒ x = 14