Let's assume your data start from row 2 (row 1 is for column headers). Select the datarange in column A and activate Conditiona Formatting;
Create a 1st rule. Select "Use a formula to determine which cells to format" (this selection goes for all rules). Enter the formula
Click <Format>, activate tab Number, select category Custom, and enter into Type field "information provided". <OK>. <OK>;
Create 2nd rule. Enter the formula
Code:
=AND($B2<>"Y";$A2<TODAY()+11)
Click <Format>, activate tab Font, and select yellow as font color. <OK>. <OK>;
Create 3rd rule. Enter the formula
Code:
=AND($B2<>"Y";$A2<TODAY()+6)
Click <Format>, activate tab Font, and select red as font color. <OK>. <OK>;
Check rules order (from top down: red, yellow, text replaced), and that Stop if True is unchecked for all rules. When different, then make needed changes;
Click <Apply>.