To solve for y, we first simplify the equation:

1.2 + 3/10y = 8/15y + 0.78

Multiply everything by 30 to get rid of the fractions:

36 + 9y = 16y + 23.4

Subtract 16y from both side and subtract 23.4 from both sides:

-7y = -13.4

Divide by -7 to solve for y:

y = 1.91