There's a quick way to answering questions like this without the need to go through the whole process of finding the terms before the #x^3# term:
Using the #color(white)()^n C_r# button, the value of #n# represents the expansion power of #9# and the #r# would be the term you want to find, so in this case, it would be #3#.
Therefore, the coefficient of the general #x^3# term is:
#color(white)()^9 C_3= 84#
However, you can only do this if the expansion is in the format of #(1+x)^n#.
To find the #x^3# coefficient for #(4-x)^9#:
#(a+x)^n=a^n+na^(n-1)x+((n(n-1))/(2!))a^(n-2)x^2+((n(n-1)(n-2))/(3!))a^(n-3)x^3+......+x^n#
Take just the #x^3# section of the binomial theorem expansion equation:
#((n(n-1)(n-2))/(3!))a^(n-3)x^3# and substitute values of #n#, #x# and #a# in where #n=9# and #x=-1# and #a=-4#:
#((9(9-1)(9-2))/(3!))(-4)^(9-3)(-1)^3 = -344064#
Therefore, the #x^3# term for the binomial expansion of #(4-x)^9# is #-344064x^3#
(Note: Factorial '!' is a product of an integer and all the integers below it. For example, #(4!)=4*3*2*1#