This is exactly how luni-solar calendars, such as the hebrew or the chinese one work. using various schemes, these calendars add x months (you’ll find x in part (c)) over the period of 12 ∗ 19 = 228 synodic months to get the total that is almost exactly equal in length to 19 solar years. that way those calendar are average synchronized with the gregorian calendar. (e) (optional) a purely lunar calendar, such as the islamic one, does not synchronize with the solar year. because of this, muslim holidays tend to drift from year to year relative to the gregorian calendar. after a number of years they will make a full circle through the gregorian calendar. how many lunar years will pass till the difference accumulates to more than one solar year?