¿Cuál es la diferencia entre "if you like" "if you'd like" y "if you prefer" "if you can" ?Puedes dar oraciones como ejemplo.

The differences between these phrases are very minor. They all have the same basic meaning.

There is no difference between "if you like" and "if you'd like". "You'd" is simply a contraction of "you" and "would". Often, you can use "you" or "you'd" interchangeably.

For "if you prefer", the word prefer/preference is asking about which option someone would like the most. Ex:
"We could walk on the beach. Or, if you'd prefer, we could hike through the forest".

Finally, "can" asks about how capable or able you are. You would use this if you were uncertain about someone's schedule/plans/abilities. For example:
"I don't know if you have homework, but if you can, would you wash the dishes?"