What is the standard form of −4x³y + 6x² + 3y² + 9

Looks like your is already in standard form

A few seconds with google disclosed:

A polynomial is said to be in its standard form, if it is expressed in such a way that the term with the highest degree is placed first, followed by the term which has the next highest degree, and so on.
For example: 14 x^4 - 5x^3 - 11x^2 - 11x + 8