Perhaps any one here can implement the circuit you paste here. But that way you are not going to learn.
Try to resole your self, since self learning is good exercise, forum members are here to resolve problem not to do your work.
Any way this time I wrote code here, even I can write whole code its not more then 10 min job, you will not learn any thing.
From below code try to know why latch is removed and also try to learn how to do sequential design in VHDL and also how to write code for Combination design.
In your case, you are not aware about these two basic thing and you are facing problem. First do enough study then experiment it that is the way you will become an engineer.
any ways you got my idea here is code.
HTH