I believe you can just remove mature seeds
from a rose
of Sharon bush and place in moist soil; adding a little milled sphagnum moss on the surface of moist soil will help prevent fungi.
You can also propagate a rose
of Sharon bush by taking 6-8" softwood (flexible) clippings in the late spring
or early summer from a mature bush. Cut at a slight angle, and trim away all but the top several leaves. Dip cuttings in a rooting hormone, and place 3" deep in a mixture of one-half general-use potting soil with one-quarter sand and one-quarter vermiculite, that has been combined well. Press firmly around the cuttings to eliminate air pockets in the soil. Take care to never allow cuttings to dry out. Roots should begin to show within 2-3 weeks.