If a rare disease with an early onset of symptoms is inherited in a way where male and female are affected equally and only homozygous persons are affected, then the likely mode of inheritance is

When male and female are affected equally, this indicate there is no predilection for male or female, This indicates that mode of inheritance is autosomal. As question says the disease only affects homozygous person and it has early onset of symptoms, this indicate the mode of inheritance is recessive. Therefore, above disease is most likely autosomal recessive disease.