Your H1 meter starts running the day you enter the US. It stops when you leave the shores of US and restarts when you enter again. The date on the H1 approval notice is meaningless. Go by the dates on the I-94's.
Also someone told me or probably I read, cant substantiate it though is that the H1 meter (6 years) limit is associated with the number if hours you put in. I.e. there are fixed number of hours your are allowed to work before your H1 limit is reached. This way you could possibly reach your H1 limit in 3 years itself if you worked 80 hours per week. At the same time if you have been working only 20 hours per week throughout then your H1 limit wont reach for 12 years. (Very good Fiction) and clever thinking. if we work for 5 hours per week , can we stay 50 year. ? brilliant thoughts If this is real then you can calculate your reamining time by adding the number of hours you have put in from your pay stubs.
But I think this is all BS as INS has no way to know this information unless it shares the database with IRS or the payroll department.
Although the number of hours worked may not be the criteria for the H1 limit, I am sure its not just the number of days you are in US. Its a bit more complicated. But just to be on safer side calculate the days in the US subtracting any days you went out for vacations etc.
Usually to be even more safe people just go by the date on first entry and calculate 6 years ahead. In that case your H1 limit is reached on 06/19/2007.
neocor