There are two bible verses cited as sources for the quote, "Through Christ all things are possible": Philippians 4:13 and Matthew 19:26. Both verses speak of the ability of man to accomplish all things through faith in God.
As translated by the King James version of the Bible, Matthew 19:26 states, "But Jesus beheld [them], and said unto them, With men this is impossible, but with God all things are possible." Philippians 4:13 states, "I can do all things through Christ who strengthens me."
Bible verses are often translated into popular quotes about life. As they are shared among individuals, the exact wording is subject to change, but the underlying meaning remains.