To solve the first equation (5/12x - 4/15x = 0), we need to find a common denominator for the fractions:

(5/12x - 4/15x = 0)

To find a common denominator for 12 and 15, we can use 60:

(25/60x - 16/60x = 0)

Combine like terms:

(9/60x = 0)

Now, solve for x:

(9x = 0)

(x = 0)

Therefore, the solution to the first equation is x = 0.

For the second equation (0.51x - 0.2x = 8/15), combine the like terms:

(0.51x - 0.2x = 8/15)

(0.31x = 8/15)

To solve for x, divide both sides by 0.31:

(x = (8/15) / 0.31)

(x = (8/15) * (100/31))

(x = 53.54)

Therefore, the solution to the second equation is (x = 53.54).