If Jesus taught his disciples how to pray, why does Paul say we do not know what to pray for?

The two passages speak of different kinds of knowing. In the Lord’s Prayer Jesus gave a pattern, “After this manner therefore pray ye” (Matthew 6:9): to whom we pray, and what comes first, God’s name, his kingdom and his will, then our daily needs, forgiveness and protection. Barnes notes that it was given as a model of the manner of prayer, not as the only words to use.

Paul is speaking of something more particular. In Romans 8 he has been writing about “the sufferings of this present time” (8:18) and the groaning of creation and of believers as they wait (8:22–23). In such trials we often do not know what to ask for: whether to pray for the trouble to be taken away, or for strength to bear it. Paul’s Greek says literally that we do not know ‘what we should pray as it is needful’. Paul himself asked three times for his “thorn in the flesh” to be removed, and was given grace instead (2 Corinthians 12:7–9). That is why the Spirit’s help is needed: he “maketh intercession for the saints according to the will of God” (Romans 8:27). The Lord’s Prayer itself makes room for this when it asks, “Thy will be done” (Matthew 6:10). So Christians know how to pray, and still need the Spirit’s help to know what to ask in each trial.