Justin gave 1/6 to his neighbour, so 5/6 remains. He kept 2/3 of the remainder in the fridge.
[[model:questions/solutions/q4325.png]]
• Neighbour → 1/6 of whole = 3/18
• Remainder → 1 − 1/6 = 5/6 = 15/18
• Kept in fridge → 2/3 × 5/6 = 10/18
• Not kept from remainder → 15/18 − 10/18 = 5/18
• Total not kept → 3/18 + 5/18 = 8/18 = $$\frac{4}{9}$$
Justin did not keep 4/9 of the cake in the refrigerator.
Check: Kept 10/18 + Not kept 8/18 = 18/18 = 1. ✓