Is it possible for individual IV-2 to be a carrier? Why?

Please help!

No, it is not.

Explanation:

Looking at this chart, this looks to me to be a case of an x-linked recessive disease.  (If you want to know how to tell, or got some context that this is not the case, let me know)

Remember that females have two x chromosomes and males have one x and one y chromosome. As this disease is recessive, this means that for a female to exhibit the disease, she must have both x chromosomes have the disease. If she only has one x chromosome with the disease, she's considered a carrier.

On the other hand, males are completely binary, as they only have one x chromosome - either their x chromosome has the disease, and they exhibit it, or their x chromosome does not, and they do not have the disease, nor do they carry it. Thus, males can also not be carriers.

A square on the chart is representative of a male, while a circle is a female. IV-2 is a square, thus he is a male. This means that he cannot be a carrier, so your answer is no.

If any of this doesn't make sense, feel free to let me know! Hope this helps.