1. Problem. Identify the transformations applied to the parent sine function to obtain $f(x) = -2\sin x$. 2. Formula used. We use the general transformed sine form $y = a\sin(bx - c) + d$. 3. Important rules. The parameter $a$ controls vertical stretch by factor $|a|$ and causes a reflection across the x-axis when $a<0$. 4. Intermediate work. Write $f(x) = -2\sin x = (-2)\cdot\sin x$ to identify $a = -2$, $b = 1$, $c = 0$, and $d = 0$. 5. Explanation. Since $|a| = 2$ the graph is vertically stretched by a factor of 2 relative to the parent $y = \sin x$. Since $a < 0$ the graph is reflected across the x-axis. 6. Final answer. Transformations: vertical stretch by factor 2 and reflection about the x-axis.