(Problem can be read here.)

Two days ago Andy still 25 but next year he will be 28.
With that much gap, his birthday must be near new year, and the only possible solution is:
Andy’s birthday is December 31, and ‘two days ago’ was December 30.

So we have conversation on January 1.

Two days ago, means December 30, Andy still 25.

Andy turned 26 on December 31.

So here we are in new year. In December 31 this year, Andy will be 27, so next year he will be 28.