Step 1: Calculate the numerator. $$0.36 \times 2.4$$ Multiply $36 \times 24$: $36 \times 20 = 720$ $36 \times 4 = 144$ $720 + 144 = 864$ Since there are two decimal places in $0.36$ and one in $2.4$, there will be $2+1=3$ decimal places in the product. So, $0.36 \times 2.4 = 0.864$. Step 2: Calculate the denominator. $$0.9 \times 0.6$$ Multiply $9 \times 6 = 54$. Since there is one decimal place in $0.9$ and one in $0.6$, there will be $1+1=2$ decimal places in the product. So, $0.9 \times 0.6 = 0.54$. Step 3: Divide the numerator by the denominator. $$\frac{0.864}{0.54}$$ To simplify the division, we can multiply both the numerator and the denominator by 1000 to remove the decimals. $$\frac{0.864 \times 1000}{0.54 \times 1000} = \frac{864}{540}$$ We can simplify this fraction. Both are divisible by 10: $$\frac{86.4}{54}$$ Now, perform the division: $$86.4 \div 54$$ $$86 \div 54 = 1 \text{ with a remainder of } 32$$ Bring down the $4$, making it $324$. $$324 \div 54 = 6$$ So, $86.4 \div 54 = 1.6$. Alternatively, we can write: $$\frac{0.864}{0.54} = \frac{864}{540}$$ Divide both by 10: $$\frac{86.4}{54}$$ Divide $86.4$ by $54$: $$54 \times 1 = 54$$ $$86.4 - 54 = 32.4$$ $$54 \times 0.6 = 32.4$$ So, $1 + 0.6 = 1.6$. The final answer is $\boxed{1.6}$.