1. The problem asks to insert two arithmetic means between 8 and 20. 2. An arithmetic mean between two numbers is a number that forms an arithmetic progression (AP) with the given numbers. 3. Let the two arithmetic means be $x$ and $y$. Then the sequence is $8, x, y, 20$. 4. The common difference $d$ of the AP is given by $d = \frac{20 - 8}{3} = \frac{12}{3} = 4$. 5. The terms are then: - First term: $8$ - Second term: $8 + d = 8 + 4 = 12$ - Third term: $8 + 2d = 8 + 8 = 16$ - Fourth term: $20$ 6. Therefore, the two arithmetic means inserted between 8 and 20 are $12$ and $16$. 7. Final answer: $12$ and $16$.