I am try to take a connection that was originally used for a fluorescent light with a black wire and a white wire and use the same two wires with a halogen light that has a white wire, a black wire, and a yellow and green wire. Is it possible to make this conversion and if so, how?
The answer depends on exactly what your old arrangement was and what the new arrangement is, photos of everything would help make this clear.
Fluorescent lights have electronics components associated with them, for example a starter and ballast. You need to identify where these are and make sure you remove them.
Many Halogen lamps also do not work directly from your normal house electric supply (e.g. 110V AC or 230V AC depending on country etc) but need a transformer. You need to be sure the bulb is rated for the full voltage or that a new light fitting includes a suitable transformer.
Some compact fluorescent bulbs and some halogen bulbs are designed for use with the standard light fittings that are/were used for ordinary traditional incandescent bulbs. In this case, the associated electronics are built into the base of the bulb. If your old and new bulbs are both of this type, you should have no need for rewiring the bulb-holder/lamp-fitting.
The green/yellow wire is for a protective earth/ground connection. This suggests that your new fitting has exposed metal parts that could present a safety hazard if a fault develops in the fitting or in the wiring supplying the fitting. You need to check the building electrical code or regulations that apply in your country/state. In the worst case, you may need to run a new earth wire or have an electrician certify that your earthing arrangements (or lack of) is safe.