This is a quadratic expression, meaning it can be factored into two binomials each with the variable to the power of one. Knowing this, we can already deduce that the factorization would look something like this:
(y + ____)(y + ______)
The blanks equal the factors of the last term. The last term may have multiple pairs of factors, but you need to look at the middle term to find the correct pair. The sum of the pair of factors should equal the middle term. For instance, in this example 8 + 1 does not equal 6, even though it is a factor pair of 8. It is easier to grasp the answer if you name all the factor pairs and work from them. With practice, factor pairs will come easier. In this case, the factor pair is 4 and 2.
4x2 = 8 and 4 + 2 = 8.
Therefore, (y + 2)(y + 4) = y^2 + 6y + 8