This is a simple proportion question, couched in the more complex language of a word problem. Since the recipe is an indication of how much of each item relative to each other item you'll need to make the sorbet come out right (i.e. the ratios of ingredients), those ratios should be the same regardless of how much you're making. In other words, they should be in proportion. Remember, a ratio is just another word for a fraction, and for two ratios to be 'in proportion' they are equivalent to each other (basically they would each reduce to the same fraction, like 4/8 and 6/12 both reduce to 1/2, and thus all three fractions are in proportion to each other).
So to find the missing quantity, in this case the number of servings of sorbet, you want to set up two fractions (ratios) and set them equal to each other. The key to proportions is to make sure you arrange the values in the right relationships to each other - the two values belonging to the original setup need to either be vertical or horizontal, but NOT diagonal to each other. I find it most helpful to state the proportion as a sentence to help me arrange the fractions. So your question I'd state like this:
"One-half of a lemon is to six people as three lemons are to how many people?"
(The phrase 'is to' is a way of referring to the proportionality of two quantities - whatever relationship the one-half lemon has to the six people, the three lemons have the same relationship to the unknown number of people.)
Also, don't be tripped up by the one-half; I'd just rewrite that as a decimal for simplicity's sake. Now you take that sentence and write your two fractions set equal to each other in the same order the quantities appear in the sentence. So the way I have it stated up there, you'd end up with the following:
0.5/6 = 3/x
But you could just as easily have arranged it the other way, i.e. your sentence would say:
"One-half a lemon is to three lemons as six people are to how many people?"
And your setup would look like this:
0.5/3 = 6/x
In one case you're stating the relationship between lemons and people, and in the other case you're stating the relationship between initial quantities and new quantities. But both are valid; just make sure like quantities are either vertical or horizontal to each other.
I'll let you solve for x from there.