the mission that Lt. Grall ask you to "Explore Strange New Worlds" where do you go to do 3 missions to explore?

Where you go doesn't matter, all that matters is that you complete an explore mission cluster Like [Explore the Delta Volanis Cluster] after you accept explore strange new worlds.
hope that helps.

I did a mission to explore 3 missions and it didnt work?

You need to accept the "Explore Strange New Worlds" mission, THEN accept the mission to explore 3 systems in a star cluster.

how would I do that? and where do I go to do it? I have no clue about this mission?

There are various quest givers who will give you a compatible mission. Lieutenant Grall gives three of them (for low level characters). For higher level characters simply consult this chart to see who you need to talk to and where to go:
http://www.stowiki.org/List_of_missions#Exploration

Okay I've got the mission to "Explore Strange New Worlds". But there is no continuation to explore 3 systems in a star cluster. What it says in my mission log is this:

I, Lieutenant Hana, or one of the other exploration contacts can direct you to the star clusters where the Federation has limited or no information about distance areas of space. Carry out our mission of exploration and expand the boundaries of the Federation's knowledge.

o Complete an Exploration Tour


Accept a mission to explore 3 systems in a star cluster, then report in after you complete the exploration.

After you except the "Explore Strange New Worlds" mission from Lieutenant Grall he is no longer in Available Missions. So there in no where to accept explore 3 systems in a star cluster from him. As for Lieutenant Hana, I haven't been able to find this NPC.

So do I just drop this Mission? Can it be taken again?

It's daily mission you can take it evry 20 hours.

I remember, a long time ago, I had the same confusion you did. If you look on your "Available" list, the same place where the "Explore Strange New Worlds" mission is located, you will see that Lt. Grall and several others offer mission to various places that involve exploring three uncharted worlds, such as "Explore the Delta Volanis Cluster". You can except the mission "Explore Strange New Worlds" and except a mission from one of these others and that's how it works. "Explore Strange New Worlds" is not really a mission in and of itself. It is a vehicle to get you to do other missions by rewarding you with Dilithium when you're done.
So, Just accept any of the missions, such as explore the Delta Volanis one and accept Explore Strange New Worlds and they run together. It doesn't matter which order you accept the missions in, this is from long experience. Once you complete the "Cluster" or "Nebula" mission, the "Explore" mission is resolved as well. You don't have to do anything else.
If you have any more questions about this or anything else, please don't hesitate to ask.

That did the trick, thanks

Captain Verina
U.S.S. Lightning