We are looking at the decomposition of hydrogen peroxide into water and oxygen gas:
2H2O2 --> 2H2O + O2
We are starting with 3.4 g of H2O2. First we need to convert this to moles. The molecular weight of H2O2 is 34 g/mol
3.4 g * (1 mol/34 g) = 0.1 moles H2O2
From the chemical equation we see that every mole of H2O2 produces an equivalent mole of H2O, so 0.1 moles of H2O2 produces 0.1 moles of H2O. We know that 1 mole of a substance is equivalent to Avogadro's number (6.022 x 10^23) of the molecules of the substance. So we multiply the number of moles by Avogadro's number.
0.1 moles * (6.022 x 10^23 molecules/mole) = 6.022 x 10^22 molecules of water
The answer is 6.022 x 10^22 molecules of H2O.