What are the domain and range of the relation (-4, 2), (o, 1), (0, 5), (8, 10)

The range is easy. It is the set of all second components of the ordered pairs, with duplicates ignored, so {2; 1; 5; 10}. That eliminates A, B, and D.
The domain is harder, especially for a relation as opposed to a function, and it confuses a lot of people. The domain is the set of all sets that you are allowed to choose from for the first component of the ordered pairs in an itemized list of of the relational pairs. In most branches of mathematics every element of the domain is to be associated with exactly one element of what is called the codomain (the codomain being the set of allowed values and the range being the set of actually use values for the second component of the ordered pairs, so the range is a subset of the codomain). Thus, for a function, you can determine the domain by listing or describing in a set all the values used as first components of the relational pairs. This is apparently what the original question writer intended the readers to do, because that enumerated set {−4; 0; 8} is part of choice C.
However, the question involves a relation, not a function. We see that 0 is related to two values (1 and 5), which is generally not allowed for a function. Even if we did not have any case of one element of the domain related to multiple elements of the range, the question tells us it is a relation. For a relation, there is no restriction on how many elements in the codomain that one element in the domain may be related to—it could be zero. Therefore, an element of the domain may not be related to any element in the codomain, and, consequently, there may not be any relational pair with that value in the first component. Therefore, you would not know that that element is in the domain just by looking at the relational pairs. This means that the correct answer is that the domain is some superset of {−4; 0; 8}.