For what value of $a$ would the following system of equations have an infinite number of solutions?

$$2x-3y=6$$ $$4x-6y=3a$$

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If two lines have infinite solutions, they must be the same line. We can double the first equation to obtain:

$$2(2x-3y) = 2(6)$$ $$4x-6y=12$$

For the two lines to be the same,

$$3a=12$$ $$a=\boxed{4}$$