I want to be sure that I am 'safe'
The only way to be sure you are safe from malware from Java exploits is to uninstall it completely. The best that can be said of the latest, most secure Java version is that it has no known security bugs.
Java has reached 1.7, so just about any 1.6 version should be considered unsafe.
the thing is that I have used yahoo and there seems to be a problem Malicious advertisements served via Yahoo
That page notes:
The investigation showed that the earliest signs of infection were at December 30, 2013. Other reports suggest it might have started even earlier.
Now let us look at Release Dates for Java 6. The last publicly available Java 6 version is:
Java SE 6 Update 45[76] 2013-04-16 42 security fixes;[77] other changes;[76] final public update[78]
Or April 16th, last year. Some 8 months before that security alert.
Like I have been saying. Every publicly available version of Java 6 should be considered suspect.
Every - single - one.
You should run a Malware checker on your machine.
But your answers & comments indicate to me something more. You don't really need to run Java applets in the browser, and probably do not need it for any other reason, so also uninstall Java completely.
And I do mean uninstall it, I do not mean not disable it, I do not mean not keep it up to date. You do not seem to need it on your PC, so don't take the risk.