Which of the following can damage a multimeter?

When a multimeter is set to measure resistance (ohms), it uses its own internal battery to apply a small voltage to the component being tested. The meter then calculates resistance by measuring how much current flows through the component. If you probe a live circuit containing its own voltage while the meter is in this resistance setting, that external voltage is forced directly into the delicate internal circuitry of the meter. This can easily overload and permanently destroy the meter's components. The other options do not pose a danger to the equipment. For example, measuring resistance on a voltage setting will simply result in a zero-volt reading without causing damage.