(2 - x)(3x + 1)^{9} = 2(3x + 1)^{9} - x(3x +1)^{9}

Consider (3x + 1)^{9}

Here, a = 3x, b = 1, n = 9

We have t_{r+1} = ^{n}C_{r}a^{n-r}.b^{r}

= ^{9}C_{r}(3x)^{9-r}.x^{9-r}

To get the coefficient of x^{6} in 2(3x + 1)^{9}, we must have

x^{9-r} = x^{6}

^{\(\therefore\) }x^{9-r} = x^{6}

^{\(\therefore\) }9 - r = 6

^{\(\therefore\) }r = 3...**...(i)**

Also, to get the coefficient of x^{6} in x(3x + 1)^{9}, we have have

x.x^{9-r} = x^{6}

\(\therefore\) x^{9-r} = x^{5}

\(\therefore\) 9 - r = 5

\(\therefore\) r = 4.....**..(ii)**

\(\therefore\) The term containing x^{6} in the expansion of