nC14=nC16 then find n

nC14 is the number of ways of choosing 14 things out of n things
which is also the number of ways of leaving 14 things behind


nC16 is the number of ways to choose 16 things out of n things
which is also the number of ways of leaving 16 things behind

Those are the same, so since

the number of ways of choosing 14 things is the same number of
ways of leaving 16 things behind, 

and

the number of ways of choosing 16 things is the same number of
ways of leaving 14 things behind,

Then there must be 14+16 or 30 things.

Checking 30C14 = 145422675 and 30C16 = 145422675 

Edwin