Carrier proteins and channels are utilized to help particles cross impermeable or selectively permeable membranes. An excellent example are ions and cellular membranes. Ions are highly charged species and cannot naturally pass through the hydrophobic membrane so special proteins embedded in the membrane must allow the ions through. Let's look at each multiple choice answer in turn.
1. Diffusion: This is the natural process of a concentrated group of particles spreading out to cover a more equal distribution. This does not require any protein carriers or channels since there is no membrane involved.
2. Facilitated diffusion: This is an example of passive transport, or diffusion across a membrane following the natural concentration gradient. This does not require any external energy but it does require carrier proteins and channels to allow passage through the membrane.
3. Osmosis: This is the transport of water through a selectively permeable membrane. Whether proteins are involved depends on the situation. If you are talking about water moving through cell membranes, then yes carrier proteins are involved.
4. Active transport: This involves particles moving against the natural concentration gradient and go from low concentration to high concentration. This requires an input of energy and is accomplished through carrier proteins and channels.
So the answer to your question is 2, 3, and 4, although 3 depends on the exact situation.