Hey, my friend was saying the Explore the Hromi cluster was a good place to get mark 3/4 gear for a LTC, but i dont have access to it, does anyone how i can get that mission?

As far as I know there is a level requirement for that mission. I don't know what level you have to be, but try talking to all "Lieutenant Something" contacts in your "Hail Starfleet" list. These dudes give those missions.