Explanation:
The genes that determine color and pattern are linked.
Homozygous lined aqua beetle has the genotype lb/lb
It can produce only 1 type of gamete: lb
X
Homozygous solid blue beetle has the genotype LB/LB
It can produce only 1 type of gamete: LB
The F1 is formed by the union of the parents' gametes, so it will have the genotype lb/LB
Test crosses involve a homozygous recessive individual.
The homozygous recessive individual lb/lb can only produce 1 type of gamete:
The F1 individual lb/LB can produce 4 types of gametes: