The mass of potassium chloride is #"3.8 g"#.
Take the balanced chemical equation
#2KClO_3 -> 2KCl + 3O_2#
Look at the mole ratio you have between potassium chlorate and potassium chloride; what you will see is that every #"2 moles"# of potassium chlorate will produce #"2 moles"# of potassium chloride, i.e. you have a #"1:1"# mole ratio between the two compounds.
The number of moles of #"KCl"# will mirror the number of moles of #"KClO"_3#, regardless of what that number is. This means that you know how many moles of #"KCl"# you'll have - exactly how many moles of #"KClO"_3# you have.
Since you were given the mass of #"KClO"_3#, you can determine how many moles you have by using its molar mass
#"6.3 g KClO"_3 * ("1 mole")/("122.6 g") = "0.051 moles"#
Automatically, the number of #"KCl"# moles produced will be
#n_("KCl") = n_("KClO"_3) = "0.051 moles"#
Now use #"KCl"#'s molar mass to determine how many grams you'll get
#"0.051 moles KCl" * ("74.6 g")/("1 mole") = "3.8 g"#
The reaction you are dealing with is the decomposition of potassium chlorate (more here: http://socratic.org/questions/what-does-kclo3-decompose-into).
