Answer:
The correct answer would be "Through a receptor on the cell membrane that transduces its signal to the cell's DNA".
Hormones produce their effects mainly by binding to their specific receptors. It leads to the formation of a hormone-receptor complex which results in certain biochemical changes on a target tissue.
These receptors can be of two types of membrane-bound and intracellular receptors.
The hormones which are protein or amine in nature are water soluble and thus can not pass through the lipid bilayer of a cell. They produce their effects mainly by binding to the membrane bound receptors. For example, insulin, growth hormone, Adrenaline, ADH, oxytocin, FSH, TSH et cetera.
Insulin binds to glycoprotein complex receptor present in the cell membrane.
In contrast, a lipid-soluble hormone such as steroidal hormone (estrogen) binds to the intra-cellular receptors as they can easily pass through the lipid bilayer.