cuttings will give an exact copy of the parent plant.... take a tip cutting. apply 0.1% IBA (rooting hormone) stick in well drained soil & mist taking 25-80 days to root.
from seed you will find many small plants arount the parent. it takes 1 year for some flowers to form & the 2nd year will be even better... so....check the flower color & keep the ones you like

Rose of Sharon seeds will re-seed themselves if there is any bare ground near the parent plant, but as yiorges-z5il says the only way to get an exact copy is through cuttings. Almost all the ones I have grown down this way are little tree-type plants that seem to grow to about 6' and don't seem to grow too much taller for many years. I always ended up with several colors, some bi-color. But for double blooms they only seem to come from cuttings. Even then I have found some revert to single type blooms, but I enjoy all colors and types as I just love flowers of all types, colors and forms.