It is a perfectly natural way to say it. Another alternative would be to use the word advance.
Let's advance the board meeting by two days. December 18 isn't working for me.
Some notes (they are already said by others, but I would repeat it nonetheless):
Your sentence is indicating pushing back the event, instead it forwarding it to an earlier date. If you intend to achieve the meeting to be held on December 20 then,
Let's push the meeting back by two days. I don't want to hold it on December 18. December 20 would work better.
On a side note: If you are mentioning the exact number of days by which the event is shifted, there is absolutely no need to include two sentences including the two dates. It is fairly redundant. If you push forward the meeting by two days, it is obvious that it will be on 16th instead of 18th now.
The following two highlighted words are mainly Indian English, but you can consider using it (if you wish).
Let's prepone the meeting by two days. I don't want to hold it on December 18.
Let's postpone the meeting by two days. I don't want to hold it on December 18.