If linkage was known at the time of Mendel then which of the following laws, he would not have been able to explain?

The correct option is D Law of independent assortment
The law of independent assortment states that when two or more characteristics are inherited, individual hereditary factors assort independently during gamete production, giving different traits an equal opportunity of occurring together. On the other hand, linkage refers to the presence of two different genes on the same chromosome. Two genes that occur on the same chromosome are said to be linked, and those that occur very close together are tightly linked. So, this would have been contradictory as Mendel would have not been able to explain the inheritance of two genes without one affecting the other.
Law of segregation or law of purity of gametes and law of dominance work for a single gene.

So, the correct answer is the law of independent assortment.