1. **State the problem:** Emma bought 12 cakes and each child received $\frac{1}{6}$ of a cake. We need to find how many children received cake. 2. **Understand the division:** Each cake is divided into 6 equal parts because each child gets $\frac{1}{6}$ of a cake. 3. **Calculate total pieces:** Total pieces of cake = number of cakes $\times$ pieces per cake = $12 \times 6 = 72$ pieces. 4. **Each child gets one piece:** Since each child gets one piece, the number of children is equal to the total pieces. 5. **Final answer:** Emma gave cakes to $72$ children.