Only end-of-course exams in courses taken for high school credit count towards graduation. So the 8th grade science SOL does *not* count for graduation, but high school students need to pass at least one high school science SOL: Biology, Chemistry or Earth Science.
If your child is taking a high-school level math class (Algebra 1 or Geometry) in 8th grade, they will take a required SOL, and if they pass that SOL, they will not need to pass another math SOL, but Arlington requires students to sit for one high school math SOL during their 4 high school years, even if they passed one in 8th grade.
In Arlington, students take World Geography for high school credit as 8th graders, and they complete Performance-Based Assessments in lieu of the SOL. If your child passes those assessments, they will not need to sit for or pass any further Social Studies SOLs in high school.
https://www.apsva.us/assessment/standards-of-learning-sol/

Virginia Standard Diploma requirements: https://www.doe.virginia.gov/parents-students/for-students/graduation/diploma-options/standard-diploma-graduation-requirements

Virginia Advanced diploma requirements: https://www.doe.virginia.gov/parents-students/for-students/graduation/diploma-options/advanced-studies-diploma-graduation-requirements

Are SOLs taken in 8th grade for science and math required for kids to eventually graduate from high school with a standard or advanced studies high school diploma?