Parallel to -7x + 6y = 8
get the y by itself
6y = 7x + 8
y = (7/6)x + 8/6
y = (7/6)x + 4/3
slope = 7/6
..going through point (-1,-4)
point-slope form
y - y1 = m ( x - x1 )
y - -4 = (7/6) ( x - -1 )
y + 4 = (7/6) ( x + 1 )
y + 4 = (7/6)x + 7/6
y = (7/6)x -17/6
or, if you want standard form:
(-7/6)x + y = -17/6
-7x + 6y = -17