If we place a fork in the right hand of a right-handed person with an intact corpus callosum
the information goes to the left hemisphere where language is processed.
If we place the spoon in the left hand of this person
the information now goes to the right hemisphere with little language ability
but the information then crosses the corpus callosum to the left hemisphere where language processing resides.
Similarly, in the visual system, if the word is flashed to the left visual field
the word goes to the right hemisphere
then crosses the corpus callosum to the left hemisphere and we can read the word.
The opposite is true for our puzzle task
If a right-handed person with an intact corpus callosum is forced to use their right hand for the puzzle
the information goes to the left hemisphere which struggles with spatial tasks
but this information can cross the corpus callosum to the right hemisphere to allow this person to solve the puzzle.