To round 3.6 to its greatest place value, we round it to 4 (since the digit after the decimal is 6, which rounds it up).
Now, we multiply the rounded number by 24:
\[ 4 \times 24 = 96 \]
So, \( 3.6 \times 24 \) rounded to its greatest place value and multiplied gives you \( 96 \).