SQL Server 2008 R2 Memory Utilization
Majorly FULL Backup job runs the time we get this alerts.DBs which are close to 1.2 TB


Memory allocated to SQL Server is 120 G and backup running is for 1.2TB + database and in such scenario of course a high page write would be done. IF this message is only coming when backup is running you might  ignore it. In your exact previous thread, I asked you to ignore it as well.

I also asked you to collect perfmon counter values using performance data collector set and this is much needed because to answer your question whether the alert actually should be considered or can be ignored depends on that. You have to have performance/system benchmark to which you can compare other results.

NOTE: Seeing the database size I can say with confidence that adding more RAM would always help. Ideally if you take my advise RAM allocated to SQL Server should be 1/3rd of total database size. RAM's are cheaper those days instead of wasting too much effort in solving an alert I suggest you to go ahead and add more RAM, that would really be worth.

If you want me to analyze the data collector result personally my website has my mail id send me the details I can help you with the analysis.