Final answer:
The molecule's transport across the cell membrane is most likely achieved through active transport, as it moves against its concentration gradient and requires ATP, distinguishing it from passive transport mechanisms.
Step-by-step explanation:
The mechanism most likely used for the transport of a small molecule across a cell membrane, given the observations that (i) the molecule moves inside the cell only, (ii) it moves up its concentration gradient, and (iii) transport stops when ATP synthesis is inhibited, is active transport. This process is characterized by the energy-dependent movement of molecules against their concentration gradient, typically facilitated by membrane-bound proteins that function as pumps.
Passive transport, in contrast, does not use energy and moves molecules down their concentration gradient. Facilitated diffusion is a type of passive transport that utilizes carrier proteins or channels to move molecules down their concentration gradient, but it does not require energy. Because the transport of the molecule in question stops when ATP synthesis is inhibited, passive transport, including simple and facilitated diffusion, is ruled out.