To solve this problem, we need to follow these steps:

1. Convert the half-gallons of milk into cups.

   • Given: $1$ cup $= \frac{1}{18}$ half gallon.
   • So, $1$ half gallon $= 18$ cups.

2. Find the total amount of milk in cups:

   • The bakery has $72$ half gallons of milk.
   • Converting half gallons to cups: $72 \text{ half gallons} \times 18 \text{ cups per half gallon} = 1296 \text{ cups}$

3. Calculate the number of cakes that can be made:

   • Each cake requires $123$ cups of milk.
   • The total number of cakes the bakery can make is: $\frac{1296 \text{ cups}}{123 \text{ cups per cake}} \approx 10.54$
   • Since the bakery can't make a fraction of a cake, we round down to the nearest whole number: $10$ cakes.

Therefore, the bakery can make 10 cakes.

Would you like more details, or do you have any questions?

Here are some related questions you might find interesting:

1. How many cups of milk will be left over after making the 10 cakes?
2. If the bakery had 90 half gallons of milk, how many cakes could it make?
3. How much milk (in cups) would be needed to make 15 cakes?
4. If the recipe is adjusted to use only 100 cups of milk per cake, how many cakes can be made with 72 half gallons?
5. What is the maximum number of cakes that can be made with 2000 cups of milk?

Tip: When dealing with unit conversions, always double-check the conversion factor to ensure accuracy.