Passage
Then will I teach transgressors thy ways; And sinners shall be converted unto thee.
Then will I teach transgressors thy ways; And sinners shall be converted unto thee.
Psalms 51:11 Cast me not away from thy presence; And take not thy holy Spirit from me.
Psalms 51:12 Restore unto me the joy of thy salvation; And uphold me with a willing spirit.
Psalms 51:13 Then will I teach transgressors thy ways; And sinners shall be converted unto thee.
Psalms 51:14 Deliver me from bloodguiltiness, O God, thou God of my salvation; [And] my tongue shall sing aloud of thy righteousness.
Psalms 51:15 O Lord, open thou my lips; And my mouth shall show forth thy praise.
The verse centers on "teach", "transgressors", "ways", "sinners", "shall", "converted", and "thee". It is saying that the verse draws attention to "teach" and "transgressors", so its meaning should be read from those terms before moving to application.
The nearby context moves from verse 12's "Restore unto me the joy of thy..." into verse 14's "Deliver me from bloodguiltiness O God thou...", so "teach" and "transgressors" belong inside that flow. In Psalms context, the local focus is worship, trust, the LORD's kingship, and covenant mercy.
A plain takeaway is to answer the verse's own emphasis on "teach" and "transgressors" with trust shaped by these words, not by a vague optimism outside the passage.