Evaluate the limit \[\lim {x\rightarrow \infty} \frac{6e^{4x}-e^{-2x}}{8e^{4x}-e^{2x}+3e^{-x}}\]
a) \[\frac{3}{4}\]
b) \[\frac{1}{4}\]
c) \[\frac{1}{2}\]
d) \[\frac{3}{5}\]
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