x-intercept means the point where the lines reaches the x-axis which means y=0
y-intercept means the point where the lines reaches the y-axis which means x=0
To find y-intercept, there is also another method which is by using the formulae itself, which is y=mx+c where c stands for y-intercept.
Regarding your question, to find y-intercept using
[y=mx+c method]
=> 7x + 8y = 18
=> y = (18-7x)/8
=> y = (18)/8 - (7x)/8
=> y = -(7x)/8 + (18)/8
:. y-intercept = 18/8
Or apply x=0
=> 8y = 18
:. y -intercept = 18/8
To find x-intercept, apply y=0
=> 18/8 = (7x)/8
=> 144 = 56x
:. x-intercept = 18/7