Left means collective property over resources (communism) which means everyone gets access according to their needs. Right means private property (capitalism) in which access to resources is defined by your wealth.

Conservative usually means authoritarian (another axis) in which some people can decide how others can live. Whether it’s via majority voting or dictated by a minority is irrelevant: anarchism (on the other side of that axis) accounts for protecting minorities as the key principle is that the lowest decision level (eg. the commune) is the one that counts.

“Liberal” can mean several things depending on the cultural/political context. Historically, it referred to a political school of freedom as opposed to centralized authority (an ancestor to anarchism). Nowadays, it can refer to the less-conservative positions (in the anglosaxon world, as opposed to conservative) or to capitalism (eg. in the latin world). From an anarchist perspective, “liberal” or “social-democrat” refers to very limited/narrow policy goals (reforms that do not attack the status quo of Nation States and private property) as opposed to revolutionary perspectives.

The political compass posted elsewhere in this thread is very informative, although more axis should be considered if you want a profound reviews of political positions. It’s interesting to note that in many cases, people whose ideas would fit in the lower-left quadrant (anarcho-communism) end up voting for politicians who overwhelmingly represent the top-right and bottom-right quadrants.