Step 1: State the concept.
A penetration enhancer is a substance that temporarily reduces the barrier resistance of the skin (mainly the stratum corneum) so a drug can pass through more easily in a transdermal system.
Step 2: Recall the classic enhancer.
Dimethyl sulfoxide (DMSO) is one of the oldest and most powerful chemical penetration enhancers. It disrupts the ordered lipid packing of the stratum corneum and acts as a co-solvent, sharply increasing drug permeation.
Step 3: Evaluate glycerin.
Option 1, glycerin, is a humectant that holds water in the skin. It is not used primarily to drive drugs through the skin, so it is rejected.
Step 4: Evaluate propylene glycol.
Option 2 (written as Propyl Glycol) does have mild solvent and enhancer action, but it is generally used as a co-solvent or carrier rather than the most potent enhancer, so it is not the best answer.
Step 5: Evaluate lanolin.
Option 4, lanolin, is an emollient and ointment base, not a recognised penetration enhancer, so it is eliminated.
Step 6: Conclude.
The most commonly cited penetration enhancer in transdermal therapeutic systems is dimethyl sulfoxide, option 3.
\[ \boxed{\text{Option 3: Dimethyl sulfoxide}} \]