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"Throughout this and last year" sounds more correct, but saying "this and last" implies two, leading me to believe "years" could be right.
This is kind of similar, but the most conclusive answer given there is "both work," so I don't have a real answer yet.
**Side note, I'm actually using the word "semester(s)," just figured using "years" is a little more generic so people looking for the same thing in the future can find this easier
The sentence is elliptical, and the missing year is assumed to exist:
Throughout this [year] and last year.
A variation would be:
Throughout this year and the last.
It's the same principle as:
I'm eating an apple and [an] orange.
If you want to make it explicitly clear, then use the full version or a different construction:
Throughout this year and last year.
Throughout the past two years.
