I'm no Chemist, but will give it a go!.
1 molecule of methane is: CH4. This means that 1 molecule of methane consists of 1 atom of Carbon 6 and 4 atoms of Hydogen 1. Since 1 atom of Carbon 6 has 6 protons and, therefore, 6 electrons. And since 1 atom of Hydrogen 1 has 1 proton and 1 electron, therefore 4 Hydrogen atoms have 4 electrons.
So, 6 electrons from the Carbon atom + 4 electrons from 4 Hydrogen atoms = 10 electrons in 1 molecule of methane, CH4.
Since 1 mole of methane has =6.023 x 10^23 molecules, therefore 1 mole of methane has:
10 x [6.023 x 10^23] =6.023 x 10^24 electrons.
There is at least one online dictionary that mistakenly gives 6.023 instead of 6.022 Rosala, so it's possible Guest#1 came across this. However, the important thing here is the process by which he/she obtained the answer - I'm sure you can easily modify the result using 6.022 yourself if necessary!