First, convert the weight at birth from pound and ounces to just ounces.
8 lb × 16 oz/lb + 9 oz = 137 oz
The baby doubles its weight in the first six months. That means its weight increases by 137 oz over 6 months. To find how much weight was gained in 4 months, write a proportion.
137 / 6 = x / 4
6x = 548
x = 91 ⅓
The baby gained 91 ⅓ oz in 4 months, or 5 lb 11⅓ oz.