Question

A woman gives birth to quadruplets or four infants. two of her children are identical twins. the other two are fraternal twins. how could this have happened

Answer 1

To explain this, let's go back to the fertilization:
The identical twins are formed by an association of one spermatozoid and one ovule to form an egg. this egg will start growing and suddenly divide into 2 eggs, to give afterward 2 individual with the same genes.
The fraternal twin comes from two different spermatozoids which will fertilize one ovule each, and give 2 different individuals sharing half of their genes.

In this case, both phenomena happened. It means there were three spermatozoids fertilizing one ovule each. And one of the eggs divided into 2 eggs. it ended by 2 eggs which are different and 2 eggs which came from the same one.