what is last tuseday
it is the tuesday from the previous week.
See, as I'm sure you're aware, most calendars separate the year into 12 months, and the month into 28 to 31 days; each month is also divided into approximately 4 "weeks", weeks occasionally "spilling over" into adjacent months. The week names are often referred to in the paste tense (Last tuesday" to indicate the tuesday of the week prior to the current week; for example, on Wednesday, last tuesday would be 8 days previous, not the day before.
The same can be done, moving forward; "Next" tuesday would be the tuesday of the next week. Note that when using such terms "next" or "last" that it refers to the weekday that is part of the previous or next week, not the one belonging to the current week.
Strangely, this same logic doesn't quite extend to Months; saying "Next December" in March, for example, might mean the December of the current year. One should ask for clarification if it's important in this case.