To solve the problem, we calculate how many cups of flour are needed for one 4-layer cake and then determine how many such cakes can be made with the available 76.0 cups of flour.

1. Flour needed for one single layer:
   $1.5 \, \text{cups/layer}$

2. Flour needed for a 4-layer cake:
   $1.5 \times 4 = 6.0 \, \text{cups/cake}$

3. Number of 4-layer cakes you can make with 76.0 cups of flour:
   $\frac{76.0}{6.0} = 12.6667 \, \text{cakes}$

Since you cannot make a fraction of a cake, you can make 12 complete 4-layer cakes.

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Would you like further explanation or additional examples?
Here are 5 related questions:

1. How much flour would remain after making 12 complete 4-layer cakes?
2. How many layers can you make with 76.0 cups of flour?
3. If a single layer required 2.0 cups of flour instead, how many 4-layer cakes could you make?
4. How much flour is required to make 15 4-layer cakes?
5. If you used 1.25 cups of flour per layer, how many 4-layer cakes could be made from 76.0 cups?

Tip: When dealing with unit-based problems, always divide the total quantity by the amount used per unit to determine the total number of units possible!