(4b^2-16) is an example of what is called a difference of squares because each term is a squared value. It has the form:
(a^2-b^2) which always factors to (a-b)(a+b)
In this case the square root of 4b^2=2b and the square root of 16=4 so its factors are:
(2b+4)(2b-4) now we can factor out 2 from both terms...
2(b+2)2(b-2) to get
4(b+2)(b-2) (answer B.)