This question is really about sorting four child care terms into the group they truly belong to: family welfare services versus juvenile justice institutions.
- Remand home placement and Foster home placement: A remand home holds a child accused of an offence while the case is being looked into. That has nothing to do with a couple accepting an abandoned child, so this pairing is wrong.
- Remand home placement and Borstal placement: Both terms here, remand home and Borstal, belong to the juvenile justice system for children in conflict with the law. Neither describes a couple accepting a child into their family.
- Adoption and Foster home placement: Adoption gives a couple full and permanent legal parenthood over the child. Foster home placement gives the child a family setting for a period without that full legal transfer. Both are genuine child welfare routes for a child who needs a home, which fits the question perfectly.
- Adoption and Remand home placement: Adoption fits, but pairing it with remand home mixes in a juvenile justice term that has nothing to do with an abandoned child being welcomed into a family.
Only the third option keeps both terms inside family based child welfare care, without borrowing any term from the juvenile justice system.
So, legal acceptance of an abandoned child by a couple falls under adoption and foster home placement.