Let's check the condition "both inputs are high (1)" for each gate:
AND gate: Output is 1 only if BOTH inputs are 1. (1 AND 1 = 1). This matches the condition.
XOR gate: Output is 1 if inputs are different. (1 XOR 1 = 0).
NAND gate: Output is the opposite of AND. (1 NAND 1 = 0).
NOR gate: Output is the opposite of OR. (1 OR 1 = 1, so 1 NOR 1 = 0).
The only gate that produces a high output (1) when both inputs are high is the AND gate.