Q:

How can the Bride tell the number of years she was in a coma by looking at her palms?

In Kill Bill Volume 1 we see the character played by Uma Thurman waking up from a coma that lasted 4 years.
The first thing she does immediately, is look at her palms and then realize that four years had passed.
Is it really possible for someone to tell how old he/she is by just looking at their palms?

A:

According to the FAQ on IMDb, it was assumed that she was taught that in her training:

In some cultures, they teach you a way to tell many different things
  just by looking at the lines of the palm. So, it is assumed that she
  read those lines to judge the amount of time she was out. Notice the
  close up shot of those lines before she says, "4 years?"

Beatrix had extensive training and education.  She could have easily been taught the art of palmistry through her training.  This would have allowed her to look at the lines on her palm to determine her age at the time that she woke up.

Learning how to identify the primary lines used in palmistry can help
  you read hands, and may help you calculate a person's age or vitality
  in life.

Beatrix learns most of her skills from Pai Mei.  This could be where she would have learned the art of palmistry.

