The genetics of racial appearance is very complex. Below is a simplified answer to this question.
Fraternal (dizygotic or DZ) twins that appear to be of different races have been described. This could happen in several different ways:
Twins that appear to be of different races could result from heteropaternal superfecundation.
DZ twins, like other siblings, share on average half of their genes. Like other siblings, they can look very similar or very different from each other. In cases where DZ twins are born to parents of different races, one twin could “take after” one parent and the other twin could “take after” the other parent.
Biracial couples can produce DZ twins where one twin looks more like one race and the other twin looks more like the other race. These parents carry genes for physical characteristics from both races. Such genes determine skin color, hair color and texture, eye color and shape, and other physical traits. By chance, the children of mixed-race parents could inherit many more of the genes typical of one race than the other race. For example, one twin could inherit more of the genes that determine darker features, and the other could inherit more of the genes that determine fairer features.