Can I use a 16-gauge adapter on a 12-gauge extension cord?

No. The adapter becomes the weak link because a 12-gauge cord handles up to 20 amps, but a 16-gauge adapter is only rated for about 13 amps. Plugging in a space heater or power tool can cause the adapter to overheat, melt, or catch fire. Always match the adapter’s gauge to the cord’s rating, or better, get the right cord without adapters.