It looks to me as if the date is 1984, although it's hard to tell. My guess would be that someone applied for a copy of the birth record in 1964 or 1984, and this is what they received. Here's what I'm reading on the document:
I (name illegible), Deputy Registrar of Births, Deaths, and Marriages for the Coast Province of Kenya, do hereby certify that the above is a true copy of the entry recorded in the Birth Register of this Province, Book [46?], Page [67??]. Given under my Hand and Seal of Office this 17th day of February, 1984.
But if this is genuine, then all one would have to do is examine the Birth Register of the province in question, Book 46?, Page 67?? and the record will be there. That, I think, is what they're asking the court to do.
That’s Book 44B, page 5733.
Obama graduated from Columbia in 1983. So maybe he needed a copy of his REAL BC to have the docs required to enter the workforce.
I strongly recommend you go to #1 and start reading. It is all explained - the document is from 1964.