Challenge: a chemical equation is balanced when each side of the equation includes the same number of each type of atom. is the equation balanced as written? why or why not? if you are familiar with balancing equations, balance the photosynthesis equation. write the balanced equation below, and then check your work ^ | | |i'm so confused

If the reactants are the same the equations are balance but if the reactants are not the same you have to make them balance, however if the reactants are not balance  in order to balance the equation you need to use coefficient to balance the reactants and products of particular chemical reaction.
yet for Photosynthesis the equation 
CO_2 + H_2O => C_6H_12O_6 + H_2O + O_2
Find the ugliest Compound in equation and do not balance first the repetitive Element.
A)So the ugliest one is C_6H_12O_6 and the C is not repetitive and have six atoms so there fore we multiply 6 as coefficient with carbon dioxide.
6CO₂+ H₂O → C₆H₁₂O₆+H₂O+O₂ but oxygen will get 12 atoms because is to all Carbon dioxide.
B) Then we have carbon balanced then we are going to balance Hydrogen, yet on product side it have 14 but on the reactant side it have 2 but Oxygen on product side is 9 there but on reactant side we have 1 so there fore we have to multiply water on reactant side by 12 and on product side multiply water with six and in addition multiply oxygen with 6 which land you at:
6CO₂+ 12H₂O → C₆H₁₂O₆+6H₂O+6O₂.
so we will have 24 hydrogen and 24 oxygen on both sides. 
Hope that helps you.