The baker used 1/3 of the eggs for cakes, so 2/3 remains. He used 1/4 of that remainder for cookies.
[[model:questions/solutions/q4328.png]]
• Cakes → 1/3 of whole = 4/12
• Remainder → 1 − 1/3 = 2/3 = 8/12
• Cookies → 1/4 × 2/3 = 2/12 = $$\frac{1}{6}$$
The baker used 1/6 of the eggs to bake cookies.
Check: Cakes 4/12 + Cookies 2/12 + Left 6/12 = 12/12 = 1. ✓