Simplifying
4y2 + -8y + -60

Reorder the terms:
-60 + -8y + 4y2

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -2y + y2)

Factor a trinomial.
4((-3 + -1y)(5 + -1y))

Final result:
4(-3 + -1y)(5 + -1y)