Final answer:
The offspring of a cross between a red rhododendron and a white rhododendron exhibit incomplete dominance, where the heterozygote phenotype appears as an intermediate between the two parents.
Step-by-step explanation:
The type of inheritance that the offspring of a cross between a red rhododendron and a white rhododendron exhibit is incomplete dominance. Incomplete dominance occurs when neither allele is dominant over the other, and the heterozygote phenotype appears as an intermediate between the two parents. In this case, the red allele is incompletely dominant over the white allele, resulting in patches of red and white in the offspring.