Equation balancing in chemistry is a demonstration of the law of conservation of mass, which states that mass is neither created nor destroyed, it just changes into different forms. A balanced equation counts the number of atoms of each element involved in the equation on both sides of the yields sign, then uses coefficients to equalize the numbers on both sides. I teach my students to use two columns, one for the reactants side and one for the products side to keep track of the numbers of atoms. Lets start with the first equation, it would look something like this:
K 1 1
H 2 3
O 1 1
If there is one inequality, as exists in the number of hydrogens, between the reactants and the products, the equation is unbalanced. Remember to adjust numbers as you insert coefficients. I would start by placing a coefficient of 2 in front of the KOH:
K + H2O ---> 2KOH + H2
That would change the atom count to the following:
K 1 2
H 2 4
O 1 2
Then I would go to the reactants side and insert a 2 for the K and a 2 for the H2O, like this:
2K + 2H2O ----> 2KOH + H2
That would adjust the atom count like this:
K 2 2
H 4 4
O 2 2
When you get all the atoms to equal, you are done!
Here are the other balanced equations, practice a little and you will get the hang of it.
4NH3 + 7O2 ---> 4NO2 + 6H2O
Mg(NO3)2 + 2LiOH ---> Mg(OH)2 + 2LiNO3
The last one is really interesting, I'll let you try it on your own!