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To subtract monomials, they have to be similar, that is to say, they must have the same literal part.

The difference of two or more monomials is another monomial whose literal part is the same and the coefficient is the difference between the coefficients.

axn − bxn = (a − b)xn

2x2y3z − 3x2y3z = 5x2y3z

The subtraction of two or more non-similar monomials is a polynomial.

2x2y3 + 3x2y3z

The explanation is correct, but in your example, the difference is wrong. Assuming the inner numbers 2 and 3 are exponents and not coefficients, the difference should be -x^2y^3z. (If they are not exponents, it should be written as 12xyz - 18xyz = -6xyz. See the difference?). The second example should be 2x^2y^3 - 3x^2y^3z., where inner numbers 2 and 3 are coefficients. :-)
Subtracting Monomials
To subtract Monomials, we have to subtract the numerical coefficients like in whole numbers, and then bring down the same literal coefficient. Take note that we can only subtract monomials having the same literal coefficient or variable.

4x - 2x 
4x + (-2x)
= 2x

4y + 2x
= 4y + 2x

7ab³ - 9ab³
7ab³ + (-9ab³)
= -2ab²