To find the area of Clarence's scale drawing of the rectangle, we first need to determine the scale factor used for the drawing.
The original rectangle measures 10 meters (greater dimension) by 6 meters (lesser dimension). In the scale drawing, the greater dimension is scaled down to 2 meters. Therefore, the scale factor can be calculated as follows:
\[ \text{Scale factor} = \frac{\text{Scale drawing greater dimension}}{\text{Original greater dimension}} = \frac{2 \text{ meters}}{10 \text{ meters}} = \frac{1}{5} \]
Next, we apply this scale factor to the lesser dimension:
\[ \text{Scale drawing lesser dimension} = \text{Original lesser dimension} \times \text{Scale factor} = 6 \text{ meters} \times \frac{1}{5} = 1.2 \text{ meters} \]
Now, we can find the area of Clarence's scale drawing using the formula for the area of a rectangle (Area = length × width):
\[ \text{Area} = \text{Scale drawing greater dimension} \times \text{Scale drawing lesser dimension} = 2 \text{ meters} \times 1.2 \text{ meters} = 2.4 \text{ square meters} \]
Thus, the area of Clarence's scale drawing is \( \text{2.4 square meters} \).
The correct answer is \( \boxed{2.4} \) square meters.