# Do ... to anger.
Nehemiah continues the prayer he began in verse 4. You may show this by making it a direct quote. "Then I prayed, 'Hear, our God, ... they are prisoners. Do not forgive ... the builders to anger.'"
# let their sin not be blotted out from before you
"do not forgive their sin" or "I do not want you to forgive their sin"
# let ... not
Nehemiah is expressing a desire.
# they have provoked the builders to anger
"they have made the builders become angry"