I have a Macbook Pro purchased in 2006. Mac OS X version 10.6.8; 2 GHz Intel core duo processor; 2GB memory. What safari browser should i update to?

Since it's a Core Duo Mac, it can't be upgraded past Mac OS X 10.6.8 and Safari 5.1.10. If you need a newer web browser on it, switch to one such as Firefox.

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In order to get a newer Safari browser, you'd have to get a later OS X system upgrade.

However the old MacBook/Pro you have probably cannot run a newest supported OS X

that has a recently updated Safari browser.

The best choice for Snow Leopard 10.6.8 would be to get and use the Firefox v 40. browser

from Mozilla, direct. It can import your bookmarks and also be set to run as a default to the

OS X by choosing that option in the old Safari preferences to select another as default. So

that means any demand for a browser would then launch Firefox instead of outdated Safari.

If you are in the US, the Mozilla Firefox link may look like this, in other regions a different URL

would be available; sometimes by just clicking on the US english page address:

https://www.mozilla.org/en-US/firefox/new/

Anyway, I'd be reluctant to attempt to buy & install Lion 10.7.5 even if it could work, as

some older applications may need to be upgraded, in some cases. Among other issues.

Your model MacBook/Pro could see an upgrade in memory, buy purchasing additional RAM

& replacement of existing chips to larger capacity exact spec chips from a reputable vendor.

PS: The first CoreDuo series has limits to upgradability, compared to Core2Duo processors.

In any event...

Good luck & happy computing! 🙂

My original MacBook (13-inch) first edition 1.83GHz coreduo is in the same situation,

and Firefox is my first choice in a supported browser. Also, for some OS X versions

that run in Intel-based Macs, there may be a suitable SeaMonkey build available...

For a fee, there is an iCab web browser which may see recent security updates.

http://www.icab.de/dl.php

Good luck in any event...! 🙂