To determine how many bags of flour Mrs. Wally Amos needs for $\frac{21}{4}$ dozen cookies, we can follow these steps:

1. Calculate the amount of flour needed for one dozen cookies:
   She uses $\frac{3}{4}$ of a bag of flour for 1 dozen cookies.

2. Calculate the amount of flour needed for $\frac{21}{4}$ dozen cookies:
   Multiply the amount of flour for 1 dozen by $\frac{21}{4}$: $\text{Flour for } \frac{21}{4} \text{ dozen} = \frac{3}{4} \times \frac{21}{4}$

   $= \frac{3 \times 21}{4 \times 4} = \frac{63}{16}$

3. Convert $\frac{63}{16}$ to bags:
   Since $1$ bag of flour equals $16/16$, we find out how many bags are needed: $\text{Bags needed} = \frac{63}{16} \text{ bags} \approx 3.9375 \text{ bags}$

This means Mrs. Wally Amos will need approximately 4 bags of flour to make $\frac{21}{4}$ dozen cookies.

Summary

Mrs. Wally Amos needs approximately 4 bags of flour.

Would you like more details or do you have any questions? Here are some related questions you might consider:

1. How much flour would she need for 5 dozen cookies?
2. If she had only 2 bags of flour, how many cookies could she make?
3. What other ingredients does she need for the cookies?
4. How long does it take to bake a dozen cookies?
5. How many cookies can she make with one bag of flour?

Tip: Always double-check your fractions when multiplying to ensure accuracy!