‘The Hebrew in Genesis 2:17 is “die die” (muwth–muwth), which is often translated as “surely die” or literally as “dying you shall die,” which indicates the beginning of dying—an ingressive sense. In other words, if they had eaten the fruit, then Adam and Eve would have begun to die and would return to dust (which is what happened when they ate in Genesis 3:19). If they were meant to die right then, Genesis 2:17 should have used muwth only once.’
Source: Bodie Hodge, “Chapter 37 – Who Sinned First – Adam or Satan?” (answersingenesis).
Read also “Sickness is A Result of The Fall“.
Note: We “inherit” physical death (= our bodies die). This is what happens to us as a consequence (not a punishment) because we have no access to the tree of life (which is Adam’s fault, not ours). NOTICE that all church fathers before Augustine affirmed: “Spiritual death (= our souls die) is NOT inherited”.