Hilbert series is a simplest way to calculate the dimension and the degree of an algebraic variety by an explicit polynomial equation. The mixed braid group $B_{m,n}$ is a subgroup of the Artin braid group $B_{m+n}$. In this paper we find the ambiguity-free presentation and the Hilbert series of canonical words of mixed braid monoid $M{B}_{2,2}$.