Decidability of Turing Machine accepting exactly 14 words
Your intuition is correct. Probably you can reduce emptiness (or maybe its complement) to this language but it's not the way I'd do it. Instead, think about how you prove that emptiness is undecidable.

You want to know if $M$&nbsp;halts on input&nbsp;$w$ so you produce a TM that accepts everything if $M$ accepts&nbsp;$w$ and rejects everything if $M$ rejects&nbsp;$w$. A slight modification of that proof will show that your language is undecidable.