Romans 3:19

‘Now we know that whatever things the law says, it speaks to those who are under the law, that every mouth may be stopped, and all the world may be brought under the judgment of God,'

The main emphasis here is on the Law as representing the Scriptures (it includes the citations above which come from the Psalms and Isaiah). But that it applies also to Gentiles is because the law that they have written in their hearts (Romans 2:14) can be seen as coming from the same source, that is, from God. In Jeremiah 31:31 the law written in men's hearts is the Law of God. They are therefore caught up in the condemnation of God's Law whether they wish it or not. All are under the Law in one way or another. So in the end it covers the Law of Moses, and the inner law of the Gentile (Romans 2:14), the main emphasis being on the Law, which is the Scriptures (compare how Jesus can speak of the whole Scriptures as ‘the Law' - Matthew 5:18; John 10:34). The first speaks to the Jews, the second to the Gentiles, but the Scriptures speak to all. All are under one law in the end, for it is God's Law. We can compare how in Isaiah 2:3 the word of the Lord streams out to the world. And that law prevents them from speaking in their own defence as they recognise that through it they are revealed as guilty. No one has any excuse to make. Every mouth is stopped. For everyone is ‘under the Law' (responsible for obedience to it) and, having failed, the whole world is brought under the judgment of God. ‘There is not one in the right, no not one'.

Note carefully the picture of the law court where the accused is brought up short. What is in mind in all this is how a man stands before his judge, the Judge of all the world. What will be given will be a legal verdict. The accused will either be declared as ‘in the right' or he will be found guilty. And Paul has demonstrated that all will be found guilty.