In an AP the difference between the 8th and the 4th term is 20 and the 8th term 1½ times the fourth term .what is the common difference

The $n$-th term of an AP is given by the formula $a_n = a + (n-1)d$, where $a$ is the first term and $d$ is the common difference.

The difference between the 8th and the 4th term is 20.
$a_8 - a_4 = 20$
Substitute the formula for $a_n$:
$(a + (8-1)d) - (a + (4-1)d) = 20$
$(a + 7d) - (a + 3d) = 20$

Simplify the equation from Step 2:
$a + 7d - a - 3d = 20$
$4d = 20$
$d = \frac{20}{4}$
$d = 5$

The common difference is 5.