How does the Reverend Arthur Dimmesdale intercede on behalf of Hester?I am reading chapters 6-11.

In chapter 3, when Hester is on the scaffold serving her
public punishment, Rev. Dimmesdale offers Hester a chance to share the name of her lover
as a means of saving her own soul and somehow diminishing her guilt and punishment.  He
knows, however, that her love is strong and she would never betray him--especially since
the usual punishment for the crime of adultery was death.  He could have interceded for
her then she neither asked nor wanted him to do so.

The two
meet again in chapter 8 at the Governor's mansion, and now she is forced to ask for his
intervention and help.  Hester has gone to deliver a pair of embroidered gloves, but her
real mission was to ensure that she would not lose her child.  There she meets Governor
Bellingham, the Rev. John Wilson, Roger Chillingworth, and the Rev. Arthur
Dimmesdale.

Rev. Wilson asks Pearl a few questions in an
effort to determine whether or not Pearl has been appropriately taught about the things
of God by her mother, a "sinner."  The young girl gives foolish answers, causing the men
to question Hester's ability to be a godly parent to this young soul.  When several of
them agree that perhaps Hester is not a fit mother for Pearl, Hester makes an appeal
directly to Dimmesdale.  "Speak thou for me!  Thou knowest--for thou hast sympathies
which these men lack--thou knowest what is in my heart....  Look thou to it!  I will not
lose the child!  Look to it!"

A nervous and emaciated
Dimmesdale is stricken by her passion, as well as his own guilt, and steps forward to
plead her case to the men who have the power (and apparently the intent) to remove Pearl
from her mother.  Despite his weakened condition, he is an eloquent speaker and his
argument is simple:  God gave this child to Hester as both a daily reminder of her past
sin and a hope for her future redemption. "To remind her, at every moment, of her fall
but yet to teach her... that, if she bring the child to heaven, the child will also
bring her parents...."

The argument, as well as the passion
with which it is delivered, is a compelling one.  Without hesitation, Governor
Bellingham agrees that Pearl should remain with her mother.  As a direct result of
Arthur Dimmesdale's intercession (help), Hester is allowed to keep her child, the only
thing she has in this world to love and cherish as her own.