Find the value of 3x to the third power - 9x to the fourth power + 6x to the third power - 2x to the second power where x=1

First write out your equation with "x" in with the highest exponent in front:

-9x⁴+6x³+3x³-2x²
simplify by adding numbers with the same exponents together
-9x⁴+6x³+3x³-2x² =
-9x⁴+9x³-2x²

When x=1, it is important to know that 1 raised to any  exponent will still always equal 1.

So, for your problem let's forget about the exponents and just plug in 1 for x.

-9x⁴+9x³-2x²
-9(1)+9(1)-2(1)= 
-9+9-2=
 -2

-9x⁴+6x³+3x³-2x² is equal to (-2) when x=1