To find the area of Neil's rectangle, we can multiply the length by the width.

1. Convert the mixed numbers to improper fractions:

   • $3 \frac{1}{2} = \frac{7}{2}$
   • $2 \frac{1}{3} = \frac{7}{3}$

2. Multiply the two fractions: $\text{Area} = \frac{7}{2} \times \frac{7}{3} = \frac{49}{6}$

3. Convert the improper fraction back to a mixed number: $\frac{49}{6} = 8 \frac{1}{6}$

Therefore, the area of the rectangle is $8 \frac{1}{6}$ square units.

Do you want any details on the calculation or have any questions? Here are some related questions you might consider:

1. How would the area change if the dimensions were doubled?
2. What is the perimeter of the rectangle?
3. How do you convert between mixed numbers and improper fractions?
4. Can you explain how to visualize area using a grid?
5. What other shapes can be used to find area, and how do their formulas compare?

Tip: Always simplify your fractions to their lowest terms for clarity!