Even multiples of 7 are always multiples of (2*7) or 14.
For example, 14, 28, 42, 56, ...
Since the square of each even multiple is less than or equal to 1,000,000, then the even multiple of 7 must be less than or equal to (√1,000,000) or 1,000.
Dividing to find the number of specified integers we get
1,000/14 = 71.428 which truncates to 71 integers.
You can also build a spreadsheet to actually find all of these integers and count them! The first is 196 and the last is 988,036.
I would like to see another approach to this interesting problem from another tutor!