Yes this helped a lot .
I exactly followed what you suggested:
X<-(82:92) ; Y<-(364:369) #####   for sellected region
> extract <- double(365) 
> setwd("C:\\Users\\aalyaari\\Desktop\\New folder (10)\\")
> listfile<-dir()
> for (i in 1:365) {
+       conne <- file(listfile[i], "rb")
+       file1<- readBin(conne, double(),  n=360*720)
+      file2<-matrix(data=file1,ncol=720,nrow=360)
+      extract[i]<-mean(file2[X,Y],na.rm=TRUE)
+       close(conne)
+ write.table(extract,"C:\\Users\\aalyaari\\Desktop\\New folder
(10)\\samregion1.txt")}

But I wonder why  I got all values like

-3.75E+306
-1.30E+54
-1.22E+58
and the right ones should be like:
22.25
22.76
33.25



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