A perfect square trinominal is the square of a binomial. Perfect square trinomials are in the form
a^2 + 2ab + b^2
or
a^2 - 2ab + b^2
Looking at the options, first check the leading term is a perfect square. They all are so we can’t eliminate anything. Next we check if the last term is a positive perfect square. The third option is not positive so we can eliminate that one.
Finally we check the center term. The first one does not have a middle term so we can eliminate that one.
The center term must be 2 times the square root of the first times the square root of the last.
The second option - square root of first term is 2m, square root of last term is 3n. 2*2m*3n is 12mn. That is not the middle term so the second option is not right.
The last option - square root of first term is 4x, square root of last term is 3y. 2*4x*3y is 24xy. That is the middle term. So the last option is the correct answer.