I also agree with what Ding said. Try to give the BB some toys to hold so that his fingers are occupied and play with him to distract him. Or let him bite a teether/soft plastic.
I let my son (8 month old now) suck the pacifier (奶咀) since 3 month old, coz I know it is much easier to quit when he grows up. 食手指 is more difficult to quit and will harm his fingers - skin & shape, as told by some experienced friends. Sometimes I saw some kids abt 4-5 years old and they still suck their fingers... really bad habit!