  The main aim of this article is to study the quantitative structure of
projective symplectic groups $PSp_{4}(q)$ with $q>2$ even. Indeed, we prove
that the groups $PSp_{4}(q)$ with $q>2$ even are uniquely determined by their
orders and the set of the number of elements of the same order. This result
links to the well-known J. G. Thompson's problem (1987) for finite simple
groups.
