Step 1: Look at the first blank. It follows 'waited' and is before 'her friend' (a person). The fixed collocation is 'wait for someone' — 'for' shows you are expecting a person to arrive. Step 2: Look at the second blank. It comes before 'the school gate' — a specific location point. Use 'at' for specific points and landmarks (at the gate, at the bus stop, at the door). Step 3: Combine both prepositions: 'waited for her friend at the school gate'. Answer: for / at