Fill a 6-inch square pot with a mixture of 3 parts medium-grit sand and 1 part peat moss. Pour water onto the soil mixture until it feels saturated at a 2-inch depth. Firm the soil mixture with your fingertips to squeeze out the excess water. Let it drain for 15 to 20 minutes before potting the hibiscus cutting.
Gather a 5- to 7-inch-long stem cutting from the tip of a healthy hibiscus branch. Choose one with a stem diameter comparable to a pencil. Use sharp, clean pruning shears to make a straight cut across the stem 1/8 inch below a set of leaves. Pull off and discard the leaves from the bottom 2 1/2 to 3 1/2 inches of the cutting.
Dip the leafless portion of the hibiscus stem into 0.1 percent IBA rooting talc. Shake it gently to dislodge any large clumps of rooting talc. Poke a 2 1/2 to 3 1/2-inch-deep hole in the center of the prepared rooting pot. Insert the hibiscus cutting into the hole and squeeze the soil mixture in against it.
Place the replanted hibiscus cutting where it will receive extremely bright yet indirect sunlight and temperatures between 68 and 75 degrees Fahrenheit. Keep the soil mixture slightly damp at all times but do not allow it to become waterlogged since the cutting might rot.
Check for roots four to five weeks after replanting the hibiscus cutting by very gently pulling on the base of the stem. If the cutting does not move, roots have formed. Keep the cutting in its pot a few more weeks before transplanting it into a larger container filled with standard potting soil.
Plant the hibiscus out in a sunny, fertile garden bed at the end of summer, or wait until the following spring if you live in an area with heavy winter frost. Water the hibiscus thoroughly after planting it out.