If the Supreme Court were to rule that marriage is a fundamental right, under the Equal Protection Clause of the Fourteenth Amendment, that would mean?

No state may distinguish between marriage and heterosexual marriage because that would effectively create invidious distinctions. This is 100% answer

I agree.

I read something today that many of us hadn't thought about. A couple is raising 4 children. However, since the state of New York doesn't recognize marriage, the couple cannot adopt children. So two of the children have been adopted by one partner and the other two children adopted by the other partner. If something should happen to one of the mothers, the other two children would have no legal parent.

If the Supreme Court were to rule that marriage is a fundamental right under the Equal Protection Clause of the Fourteenth Amendment, it would mean that any laws or practices that discriminate against same-sex couples when it comes to marriage would be unconstitutional.

To understand the reasoning behind such a ruling, we need to look at the Equal Protection Clause of the Fourteenth Amendment. The Equal Protection Clause states that no state shall deny any person within its jurisdiction the equal protection of the laws. This means that every person should be treated equally under the law, without discrimination based on certain characteristics such as race, gender, or nationality.

If the Supreme Court were to interpret the Equal Protection Clause to include the right to same-sex marriage, it would mean that denying same-sex couples the right to marry would be considered discriminatory and a violation of their constitutional rights. The Court would likely find that there is no legitimate government interest in denying same-sex couples the right to marry and that doing so perpetuates inequality.

It's important to note that this answer is based on a hypothetical scenario and does not reflect any actual Supreme Court ruling on the matter. The Supreme Court did, however, rule in 2015, in the case Obergefell v. Hodges, that same-sex marriage is a fundamental right protected by the Constitution under the Due Process Clause of the Fourteenth Amendment.