The expression is really asking what two numbers when multiplied come to 4 and when subtracted from one another come to 3? The answer is, of course, 4 and 1. So that starts the factorisation. The answer must look like (m+an)(m-bn). When we expand this we get: m^2-bmn+amn-abn^2. This can be written m^2+(a-b)mn-abn^2. We already know what a and b are: they're 1 and 4, but which way round? Looking at the expression again we see the middle term has a coefficient of +3, so a-b=3; therefore a must be bigger than b, making a=4 and b=1. This makes the factorisation (m+4n)(m-n).