$\begin{array}{l}\text{Let the number be }x\text{.}\\ \\ \text{So,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{2}{3}\times 75\%of600-x=120\\ \\ \Rightarrow \frac{2}{3}\times 75\%\times 600-x=120\\ \\ \Rightarrow \frac{2}{3}\times \frac{75}{100}\times 600-x=120\\ \\ \Rightarrow \text{\hspace{0.17em}\hspace{0.17em}300}-x\text{\hspace{0.17em}=120}\\ \\ \Rightarrow x\text{= 300}-1\text{20= 180}\end{array}$

Hence, Option A is correct.