Darius I, who ruled the Persian Empire from 522 to 486 BCE, implemented several key measures to strengthen the empire's economy. One significant action he took was introducing a common currency. This move facilitated trade and commerce across the vast territories of the empire, allowing for more efficient transactions and helping to unify the different regions under Persian control.
While increasing tribute and tax collection from various provinces did occur under Darius to maintain the empire's finances, the introduction of a standardized currency is considered one of his most impactful economic reforms. The other options listed—taxing the Great Royal Road and wiping out Zoroastrianism—are not accurate representations of Darius's economic strategies or actions.
Thus, the correct answer is by introducing a common currency.