During a constant-pressure process, the system releases heat to the surroundings. does the enthalpy of the system increase or decrease during the process?

The answer to this question would be: decrease
If the process is releasing heat to the surrounding, that means it should be an exothermic process. In the exothermic process, the process enthalpy difference will be minus because some of the energy is released as heat. That means the enthalpy of the system will be decreased.