1/6x+42+2/5x-8/3x-19=

(x/6) + 42 + (2x/5) - (8x/3) - 19

Change the denominators (numbers below the fraction bar to a to a common number for the three numbers: 6, 5, and 3 ... in other words to a number that is divisible by all three numbers)

(5x/30) + (12x/30) - (80x/30) + 23

(-63x/30) + 23

And the answer is ...

(-21x/10) + 23