3y² + 5y - 8 = 0 That is supposed to read 3y squared.
I must solve the equation(i.e. x=4 0r 6). 

3y² + 5y - 8 = 0

Multiply the red 3 by the green 8.  Get 24.

Think of two numbers such that when you

(1) MULTIPLY them, you get 24

(2) SUBTRACT them, you get the blue 5. 

Note:  [For other problems, if the sign before the green 8 had been +
instead of -, step (2) would have been "ADD" instead of "SUBTRACT".)

These numbers are 8 and 3, because when you
multiply 8 by 3, you get 24 and when you
subtract 8 - 3, you get 5.

Replace the blue 5 by (8 - 3)

     3y² + 5y - 8 = 0

3y² + (8 - 3)y - 8 = 0

Remove the parentheses by using the
distributive principle:

3y² + 8y - 3y - 8 = 0

Factor y out of the first two terms:

y(3y + 8) - 3y - 8 = 0

Factor -1 out of the last two terms:

y(3y + 8) - 1(3y + 8) = 0

For clarity I will color the two parentheses purple

y(3y + 8) - 1(3y + 8) = 0

Notice that the two purple factors are the same:

Take out the purple factor and leave the black factors in 
another parentheses:

(3y + 8)(y - 1) = 0

(3y + 8)(y - 1) = 0

Set the expression within the first parentheses equal to zero:

3y + 8 = 0
    3y = -8
     y = -8/3

Set the expression within the second parentheses equal to zero:

 y - 1 = 0
     y = 1
 
So there are two solutions: y = -8/3 and y = 1

Edwin