1. **State the problem:** We need to find the area of the base $B$ of a rectangular prism. 2. **Identify the base dimensions:** The base is a rectangle with length $6$ yd and width $2$ yd. 3. **Formula for the area of a rectangle:** $$B = \text{length} \times \text{width}$$ 4. **Substitute the values:** $$B = 6 \times 2$$ 5. **Calculate the area:** $$B = 12$$ 6. **Interpretation:** The area of the base $B$ is $12$ square yards. Therefore, the area of the base $B$ of the prism is $12$ yd$^2$.