The expression has three monomials: 2xyz, 3x2y and 4y2.
The numerical coefficients of the given monomials are 2, 3 and 4. The greatest common factor of 2, 3 and 4 is 1.
The common literal appearing in the three monomials is y.
The smallest power of y in the three monomials is 1.
The monomial of common literals with the smallest powers is y.
​Hence, the greatest common factor is y.