Thanks for correcting my grammer. I knew it was wrong after I had posted it and saw what I wrote :>)
Believe means exactly what it means. Believe in the Lord Jesus Christ. Believe that he is your savior. Believe that he is the Son of God. Believe that he has the power to save you from your sins. Believe that he says that your sins are forgiven... believe.
Sin is another matter than belief. You can believe and still sin, because the sin nature is still in your body. As Paul says... that which I know I am supposed to do, I do not, and that which I am not to do, I do. Jesus knows our sins, and has taken them away, forever. The ones we did, the ones we do now, and the ones we will do in the future. Jesus didn’t say that he saves us from some of our sins, he said he had come to save us from our sins. (all of them)
What sanctification is, is the Holy Spirit working in us to help us in our weakness.
So how do you interpret Luke 6:46? It appears from the text that Jesus said, somethign is required of you more that mere belief in Him being Lord and Savior.