Galatians 6:16, "As many as walk by this rule, peace and mercy be on them, and on God’s Israel," is a benediction or blessing Paul bestows upon those who adhere to the central message of his letter to the Galatians. Let's break down what this verse means:

"As many as walk by this rule...": The "rule" refers to the principle or standard Paul has been emphasizing throughout Galatians. This rule is faith working through love (Galatians 5:6) and the new creation (Galatians 6:15).
Paul is referring to the truth that righteousness comes not through adherence to the Law of Moses (especially circumcision, which was a contentious issue in Galatia), but through faith in Jesus Christ. He's emphasizing that it's about a transformed heart and life produced by the Holy Spirit, not external rituals.
"Walk by" is a metaphor for living out one's life in accordance with. So, it's about consistently living according to the truth of the gospel.

"...peace and mercy be on them...": This is a blessing, a prayer, or a wish that peace and mercy will be granted to those who walk by this rule.
Peace (eirene) signifies wholeness, well-being, harmony, and reconciliation with God.
Mercy (eleos) signifies compassion, forgiveness, and undeserved grace.
Paul is asking God to shower these blessings upon those who embrace the true gospel.

"...and on God's Israel.": This is the most debated part of the verse. Who is "God's Israel"? There are primarily two interpretations:
Spiritual Israel: This view holds that "God's Israel" refers to all believers in Christ, both Jews and Gentiles, who are united in faith and are part of the "new creation" (Galatians 6:15). In this view, the church is the true Israel of God, fulfilling the promises made to Abraham through faith in Christ. This is the more common interpretation among many Protestant denominations.
Ethnic Israel: This view maintains that "God's Israel" refers to the Jewish people who believe in Jesus Christ. While emphasizing the importance of faith in Christ, this view also recognizes a continuing role and promise for the Jewish people in God's plan.
Context in Galatians favors the 'Spiritual Israel' interpretation: Paul's argument throughout the letter is that salvation comes through faith in Christ, not through ethnic identity or adherence to the Law. He's trying to dismantle the idea that Gentiles need to become Jewish (i.e., be circumcised) to be part of God's people. Therefore, it makes sense that "God's Israel" refers to all believers in Christ, regardless of their ethnic background.

In summary, the verse means:

Paul is offering a blessing of peace and mercy upon all those who live according to the gospel of grace, who understand that salvation comes through faith in Jesus Christ and results in a transformed life of love. This blessing extends to all who are part of God's true people, whether they are Jews or Gentiles who believe in Christ.

Key takeaways:

Salvation is by grace through faith, not by works of the Law.
The gospel leads to a transformed life of love.
The blessing of peace and mercy is for all who believe in Christ.
"God's Israel" likely refers to all believers in Christ, united in faith, regardless of their ethnic background.