Divide two into four and Divide two by four

OP's confusion arises because "divide 2 into 4" is an idiomatic usage meaning perform a division operation, using 2 as the divisor, and 4 as the dividend.

symbolically...
4/2 = 2

clearest verbal form...
divide 4 by 2, giving the answer 2

idiomatic alternative...
divide 2 into 4, giving the answer 2

It's not the same usage as dividing a pizza into 4 [pieces], where you'd probably get 1/4 (a quarter) of a pizza as your share!

In math the term divide may have two different senses.

1) To use (a number) as a divisor. E.g: divided 5 into 35 = 7

5 is the divisor.

2) To subject (a number) to the process of division [by a divisior]. E.g: If you divide 6 by 2, you get 3

2 is the divisor.

10 divided into 100 = 10
100 divided by 10 = 10

Please check divide.