1. **Problem Statement:** Find which of the given numbers lies between $\frac{3}{4}$ and $\frac{7}{8}$.\n\n2. **Step 1: Convert fractions to decimals for easier comparison.**\n$\frac{3}{4} = 0.75$\n$\frac{7}{8} = 0.875$\n\n3. **Step 2: Convert each option to decimal:**\n- $3 = 3.0$\n- $\frac{5}{6} = 0.8333...$\n- $\frac{11}{12} = 0.9166...$\n- $\frac{19}{24} = 0.7916...$\n\n4. **Step 3: Check which decimals lie between 0.75 and 0.875:**\n- $3.0$ is greater than 0.875, so no.\n- $0.8333...$ is between 0.75 and 0.875, so yes.\n- $0.9166...$ is greater than 0.875, so no.\n- $0.7916...$ is between 0.75 and 0.875, so yes.\n\n5. **Step 4: Conclusion:** The numbers $\frac{5}{6}$ and $\frac{19}{24}$ lie between $\frac{3}{4}$ and $\frac{7}{8}$.\n\n**Final answer:** $\boxed{\frac{5}{6} \text{ and } \frac{19}{24}}$