What animal produces male gametes by mitosis?
In organisms which have haploid males (such as honeybees), there is a variation of meiosis during spermatogenesis. The meiosis-I is abortive i.e. the chromosomal events such as crossover and separation of homologous chromosomes, do not happen. However, some cytological changes do happen which is described by Sharma et al (1961) as "simulation of the normal meiosis I". This is followed by meiosis II (which is mechanistically same as mitosis). So, basically there is no halving of the number of chromosomes and the gametes are also haploid. 

So, as far as I can guess, the question in your exam sheet probably refers to spermatogenesis in Hymenopteran haploid males.



Reference: 
Sharma, G. P., Brij L. Gupta, and C. G. Kumbkarni. "CYTOLOGY OF SPERMATOGENESIS IN THE HONEY‐BEE, APIS INDICA (F.)." Journal of the Royal Microscopical Society 79.4 (1961): 337-351.