In an AP, $a_{20}-a_8=-54$. Find the common difference.

$a_{20}-a_8=(a+19d)-(a+7d)=12d$, so $12d=-54$ and $d=-4.5$. There are 12 steps between the 8th and 20th terms, not 8 (which would give -6.75) and not 24 (which would give -2.25); the value 4.5 loses the sign, but the AP is decreasing.