How can you make the moon go around in a bigger circle

You would have to give it more mechanical energy.

Like, strap a bunch of powerful rockets to one side of the moon, with all of them pointing in the direction that the moon is already moving in its orbit.  Then blast away.

NOTE:  There aren't enough rockets or rocket fuel on Earth to make a difference, even if you used ALL of them.  The mass of the moon is about

73,476,730,900,000,000,000,000 kilograms

(rounded to the nearest hundred trillion kilograms.)

That's a lot.