The correct answer is [A] locating
By saying you’re “having a hard time” you’re letting someone know that you’re having difficulty with something. This could be something physical or mental; something that could be overcome with effort. Thus, by stating “We had a hard time locating your luggage”, you just told the owner of the luggage that you made an effort to find it because it’s not easy to find a lost luggage in the airport.
These expressions should be followed by the verb-ing form (gerund):
– have fun
– have a good time
– have trouble
– have a hard time
– have a difficult time
Take a look at these examples:
• We had a lot of fun playing games at picnic.
• I had a good time enjoying my trip to Bali.
• He had a hard time finding her address.
• She’s having a difficult time finishing her school project.