The $(r + 1)$ th term of an expansion of
$(x+a)^{n}=^{n}C_{r}x^{r}a^{n-r}$
Let $(r+1)^{th}$ term be the constant term in the expansion of $(x-\frac{1}{x})^{6}\cdot$
$\therefore T_{r+1}=^{6}C_{r}x^{r} (-\frac{1}{x})^{6-r}$
$=(-1)^{6-r}\cdot^{6}C_{r}x^{r}x^{-6+r}$
$=(-1)^{6-r}\cdot^{6}C_{r}x^{2r-6}$
Since, this term is a constant term
$\therefore 2r − 6 = 0$
$\Rightarrow r = 3$
$\therefore T_{4} = (-1)^{-3} \,{}^{6}C_{3}$
$=-20$