Basic question on calculating unemployment rates
No, it's not correct. You are supposed to exclude people in FTE from labour force. Unemployment rate is a proportion of labour force which is unemployed. Labour force is defined as a sum of those employed and those looking for jobs (so it also excludes pensioners, parents on parental leave etc.). In your example the labour force should consist of only the people 16-24 years old.

I.e. $$12.2\% = \frac{\text{unemployed who are 16-24 years old}}{\text{labour force who are 16-24 years old (employed + unemployed)}}$$

Edit: I added that in this example labour force is restricted to specified age group.