Six years ago the average age of a family of 4 was 26 years. A baby was born into the family, and today the average age of the 5 of them is still 26 years. How old is the baby?

Six years ago the four members totalled $4\times 26=104$ years. Each has since gained 6 years, so today those same four total 104 + 24 = 128 years. The five members today total $5\times 26=130$ years, so the baby is 130 - 128 = 2 years old. 4 comes from ageing all FIVE members over the six years (adding 30 instead of 24) - the baby did not exist for the whole span. 6 assumes the baby arrived at the very start of the period. 26 simply repeats the average.