The order in that sentence is a claim: gratitude first, peace second. Worth testing, because most people try it the other way round — get calm, then feel thankful — and end up waiting on a calm that never quite arrives.
Gratitude is the more available of the two. You can list three real things while still anxious. You can't will yourself peaceful.
It works because attention is limited. Whatever you're genuinely appraising, you're not simultaneously rehearsing.
If your mind is loud right now, don't try to quiet it. Give it something specific and good to look at instead.