The least common denominator is the smallest whole number that the denominators 2, 3 and 4 all divide into without a remainder.
If we take each numerator separately in turn and divide each by 12 you will see how it works:
18/12=3/2; 12/12=1; 8/12=2/3; 21/12=7/4.
For example, 18/12 cancels down by dividing top and bottom by 6:
6×3/6×2; and 21/12 cancels down by dividing top and bottom by 3: 21/12=3×7/3×4.
Now let’s go back to the original:
3/2+1+2/3+7/4.
To find out what the numerator for 3/2 should, divide the denominator 2 into the common denominator 12 and we get 6. We then multiply this by the numerator 3 to get 18, so 3/2=18/12. Similarly with the others. 1 is easy because it’s just 12 twelfths: 12/12.
So all the fractions now have the same denominator 12 and all we have to do is add all the new numerators together to get the result.
I hope this helps you to understand.