OHHHHH! I KNOW THIS! YASSSS! (okay. calming meself)
Basically, the y-intercept is the point where the line crosses the y-chart-line.
#1) In #1, it is 6 because the line crosses through where the 6 point would be
#3) In #3, it is -8 because the line hits the -8 point
#2) In y = x + 7, consider it 1y = 1x + 7
In those equations, the number without a variable is considered the y-intercept (so it's 7)
#4) In y - 2x = 4 it can also be 1y = 2x - 4
It is the same rule as #2 so the y-intercept is 4