In order to determine the number of student that becomes nurses from 1566 students, take into account that the proportion must be equal for any number of total students.
The given proportion is 2 out of 12 of the current students, which can be written as 2/12. If x is the number of student which become nurses from 1566 students, it is necessary that the proportion x/1566 is equal to 2/12.
Then, you have:
2/12 = x/1566
solve the previous equation for x, just as follow:
2/12 = x/1566 multiply both sides by 1566
(2/12)(1566) = x
x = 261
Hence, the number of students which become nurses is 261 student