A Large creature on a 5-foot square grid map occupies a 2-by-2 square space. If the creature can move up to 30 feet, and each square on the grid is 5 feet by 5 feet, does the creature move up to 6 squares or 12 squares?
Movement speed doesn't have any scaling or multiplier based on size
Movement doesn't scale based on size/space - no matter how big the creature is, if it has a movement speed of 30 feet, it can only travel up to 30 feet (six squares at the standard grid scale), so if for instance it travelled in a straight line the front of it would be 30 feet from where it started.
If it helps, imagine that the part that's actually moving is the centre of the creature's space. The path taken by that centre point must fit in the creature's 30 foot movement speed, and you can step the centre point (either the intersection of grid lines for an evenly-sized space, or the central square for an oddly-sized one) around the grid as if it were a normal medium-size creature to calculate how far it can move (keeping in mind, of course, that the creature's actual size must fit through whatever path it takes!)