Anytime you have an even number of minus signs, the equivalent is a plus sign. This is equivalent to
... -6 +7 = +1
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If you want to play around with the number line, you can find -6 at 6 units to the left of zero. Likewise, -7 is 7 units to the left of zero.
Whenever you add numbers on the number line, you go in the direction they are from zero. Both 1 and 2 are to the right of zero, so when you add 1 and 2 you go 1 unit right, then another 2 units right.
If you were to add 1 and -2, you start by realizing that -2 is to the left of zero. So you go 1 unit to the right (add 1), then 2 units to the left (add -2). The result is -1.
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When you subtract a number on the number line, you go the direction opposite that number is from zero. (Essentially, you add its opposite.) In your problem, you have numbers -6 and -7, both to the left of zero. When you start from -6 and subtract -7, you go 7 units to the right, since that is the opposite direction that -7 is from zero.
Staring at -6 and going 7 units right, you end at +1.
When subtraction is written as adding the opposite, your problem is written
... -6 + (+7) = -6 +7 = +1