First, group like terms together: -16x^4y^3+4x^3y^4+36x^4y^4.
The lowest power of x is x^3 and the lowest power of y is y^3, so the highest common xy factor is x^3y^3.
The highest common numerical factor is 4. So the common factor is 4x^3y^3.
Factorisation is:
4x^3y^3(-4x+y+9xy).
We arrive at each term by dividing by the common factor: for example 36x^4y^4 divided by 4x^3y^3 is 9xy because 36/4=9, x^4 divided by x^3 is x and y^4 divided by y^3 is y so the quotient is 9xy. 36x^4y^4=(4x^3y^3)(9xy). The common factor sits outside the brackets and the quotient goes inside.