How many solutions does the system 2x + 3y = 6 and 4x + 6y = 18 have?

Multiply the first equation by $2$: $4x+6y=12$. The second equation says $4x+6y=18$. The same expression cannot equal both $12$ and $18$, so the system is inconsistent, with no solution, choice D. Graphically, both lines have slope $-\frac{2}{3}$ but different intercepts, so they are parallel and never meet. Choice A (infinitely many) would happen only if the second equation were $4x+6y=12$, the same line. Choices B and C would require lines with different slopes, since two distinct lines cross at most once.