I'm studying from my regular KJV bible and Peshita-Aramaic version of the Bible in Romans 14 and first 3 verses of 15. I have been studying the word "meat" and it's usage, meaning, etc. I'm confused as to what the meaning is. Please give me your opinion so that I can accurately understand these chapters .

You could use a good Bible commentary. Some excellent ones are reviewed at:

http://www.bibletexts.com/reviews

Also another aid to your study would be an English translation that provides an easy to understand, yet accurate, rendering of the original Greek text. The Good News Bible (Today's English Version), produced by the American Bible Society, is an excellent choice and is backed by impeccable scholarship. Links to reviews of that and other Bible versions also may be found on the webpage listed above.

Since the entire New Testament was originally written in Greek, the Syriac-based Peshitta version (Lamsa's?) is of no particular advantage, especially for the letters of Paul, who wrote and spoke in Greek to a largely Greek-speaking audience.

For an immediate answer to you question, you are welcome to browse "Rom 14:1 - Rom 15:3 - abstaining from meat and alcohol" at:

http://www.bibletexts.com/verses/v-rom.htm#14