For which of the following routes must the Z-track method be applied?

The Z-track method is specifically designed for administering intramuscular injections. This technique is employed to minimize tissue irritation and prevent the medication from leaking back into the subcutaneous tissue. By pulling the skin and soft tissue laterally and then injecting the medication into the muscle, the Z-track method creates a sealed pathway that helps ensure the medication is deposited deep into the muscle tissue, reducing the risk of leakage and irritation at the injection site.

In contrast, the other routes mentioned do not require this technique. Subcutaneous injections are administered in a different manner that does not necessitate such precautions, intravenous injections involve placing a catheter into a vein for immediate effects and do not involve tissue leakage concerns, and oral medications do not involve injections at all. The Z-track method is, therefore, uniquely applicable to intramuscular injections, making it the correct answer.