If a<0 and the product of a and b is positive, b must also be less than zero.
b=2a+4
ab=48, using b from above
a(2a+4)=48
2a^2+4a=48
2a^2+4a-48=0
2a^2+12a-8a-48=0
2a(a+6)-8(a+6)=0
(2a-8)(a+6)=0, since a<0
a=-6, since b=2a+4
b=-8
So the two numbers are -6 and -8.