The reason for this is related to a basic idea in economics, the law of demand. The law of demand tells us that when the price of a good or service goes up we will, all other things being equal, use less of that thing.
A gasoline tax would increase the price of gas. This would reduce consumption of gas to some degree. A reduction in the consumption of gasoline would lead to lower emissions of greenhouse gases. In that way, an increase in the excise tax on gasoline would raise the price of gas, thus decreasing gas consumption and emissions of GHGs.