many possible segmentations here. I would use a "top-down" approach starting from the population (e.g. 320 Millions)
I think the most useful segmentation is the one that allows you to easily came up with "backupped" answer based on your experience (on lipstick). Therefore I would choose gender and age over gender and income since for me it is easier to come up with a % of woman using lipstick in an age range than in a income range.
I would therefore
1) Start with gender (approximately xx % women in US) -> [Total Women in US]
2a) Break down by age (e.g. under 15 age no lipstick) and backup a "top-down" assumption about the % of women using lipstick in each age bracket based on experience, data, whatever you know( I would ask the interviewer before going on segmenting too much - just stop at the right level) -> [Total women using lipstick in the US]
3) Come up with a # of lipstick owned per women using Lipstick -> [Total lipstick owned in the US] = [Total wome using lipstick in the US] * [avg. # of lipstick owned / woman]
4) Remember they are asking about "every year" so it is annual sales. Therefore use the "useful life" rule to divide the [total lipstick owned in the US] by the months / years it takes to consume (or stop using) a lipstick
Hope this helps.