The given monomials are:
[tex]\begin{gathered} 18x^3y \\ 30x^2y^2 \end{gathered}[/tex]Factorizing each term, we get,
[tex]\begin{gathered} 18x^3y=2\times3\times3\times x^2\times y \\ 30x^2y^2=3\times2\times5\times x^2\times y^2 \end{gathered}[/tex]Therefore, the GCF is,
[tex]\text{GCF}=6x^2y[/tex]