There are 1.204 x 10^24 atoms of hydrogen present in 18 grams of water. In order to calculate this, it is necessary to compute the number of hydrogen moles present in the sample.
A molecule of water consists of a single atom of oxygen and two atoms of hydrogen. Oxygen has an atomic weight of 15.9994. One mole of oxygen, therefore, has a mass of just under 16 grams. Hydrogen has an atomic weight of 1.0079, and so a mole of hydrogen weighs just over 1 gram. This means that 18 grams of water contains one 16-gram mole of oxygen and two 1-gram moles of hydrogen. The number of particles in a mole is a constant known as Avogadro's number, which has a value of 6.022 x 10^23. Two moles of hydrogen, therefore, is double Avogadro's number.