The denominators are 2, 4 and 28. Both 2 and 4 go into 28, so it's the LCD.
Multiply the whole equation through by 28: this will make the fractions disappear:
14-21m+196=112m-252-m (where there's a fraction, divide the denominator into 28 then multiply by the numerator; anything that is not a fraction we simply multiply by 28);
add 21m to each side: 210=111m+21m-252 (tidy some of the numbers and m terms at the same time);
add 252 to each side: 462=132m, so m=462/132=7/2 because 66 goes into top and bottom and therefore cancels out. The reduction of the fraction can be done in steps: 462/132=231/66=21/6=7/2. Answer: m=7/2 or 3 1/2 or 3.5.