1. ponder over: After under-graduation, it takes me a lone time to ponder over about applying for post-graduation or seeking a job. I'm not sure what "under-graduation" is (it is not a usual English term). I would say that one ponders over a noun, not usually about a verb. So I might say, After graduation, it takes me a long time to ponder over my choice between a job or or post-graduate studies. 2. lay aside: Faced with the invitation to go shopping from my friend, I chose to lay aside my study plan and go out with her. This is good. I might rephrase: Faced with the invitation from my friend to go shopping, I chose to lay aside my study plan and go out with her. The reason for this is that there is less ambiguity somehow (less confusion what may be meant). 3. in the course of: In the course of his speech, I learned a lot about psychology. This is perfect. 4. have an encounter with: I had an encounter with Mike today. I have had many encounters with people who were warm-hearted. This is perfect. 5.matters of consequence(does it mean very important thing?) When we make a plan, we had better to give priority to the matters of consequence. Yes. 6. close at hand(very near to me?) The traffic accident took place today is close at hand. Correction (different from the equally good correction in the other answer): The traffic accident that took place today was close at hand. Since the accident was in the past, it cannot be close at hand in the present. However, the term "close at hand" is a metaphor, "close enough to grab with your hand". A traffic accident is not the sort of thing one might apply this too, as one does not grab or want traffic accidents. One is more likely to say, "I keep my pen close at hand" since it is something you may want to have quickly. This usage, referring to something you may want to be able to get easily, even metaphorically, is the main usage. Another example: "It is good to have friends close at hand."