a) For this question you're only interested in the k component as that measures the up-and-down-ness.

If the particle is moving downwards, it means its vertical velocity (rate of change of the k component w.r.t. t) is negative.

So, differentiate the k component w.r.t. t (that is, the and see whether what you get can ever be negative.

b) For it to stop moving, the components of i, j and k must all have zero velocity.

So differentiate all components w.r.t. t and see if there's a value of t that will make all of these zero at the same time. My suggestion is that I rather think there isn't.

c) Simply solve the equation in t that puts the k component equal to 12. You'll have a quadratic to solve.

d) Plug the value of t into tha equation you got in a) and see what you get.