One of the interesting things about patterns for the 6″ and 4″ looms is that they’re not totally interchangeable. There’s probably a formula, but you’d have to do calculations of some kind. Math is not where my windswept mind likes to settle.
Another thing to consider is the size factor. What looks good on a 4″ square may look overly busy or boring on a larger square.
Here is one of my favorite 4″ weaving patterns adapted for the 6″ loom. It’s called “Horizontal Xs (modified for 6″).” I haven’t tested this one yet, but I’m reasonably sure it will produce an interesting all-over texture pattern.