(48x^5y^3 - 18x^3y^6z) / (6x^4y^3)

First, simplify the numerator:

48x^5y^3 - 18x^3y^6z
= 6x^3y^3(8x^2 - 3y^3z)

Now divide by the denominator:

(6x^3y^3(8x^2 - 3y^3z)) / (6x^4y^3)
= (8x^2 - 3y^3z) / x
= 8x - 3y^3z/x
= 8x - 3yz^2

Therefore, the simplified expression is 8x - 3yz^2.