In order to factorize the given expression, we find to find two numbers p and q such that:

p + q = 14, pq = 48

Clearly,

8 + 6 = 14, 8 (6) = 48

Therefore, split (14a) as 8a + 6a

Therefore,

a² + 14a + 48 = a² + 8a + 6a + 48

= a (a + 8) + 6 (a + 8)

= (a + 6) (a + 8)