Melanie made a circular necklace. She puts beads evenly spaced around the necklace. If the 4th bead is directly across from the 11th head, how many beads are on the necklace

If the 4th lies opposite the 11th, then you know the 3rd lies opposite the 10th, the 2nd opposite the 9th, and the 1st opposite the 8th; meanwhile, in the reverse direction you'd find that the 5th lies opposite the 12th, the 6th opposite the 13th, and the 7th opposite the 14th. Move up one more bead and you're back at the 1st, which you already know lies opposite the 8th. Therefore there are 14 total beads.