How did I get this answer please.

2x=3y+4 and x-5y=6
find the point of intersection for each of the following pair of lines. I know the answer is (1,-2) but how?

This is called finding the solution to the set of equations. There are various ways. One way would be to graph both lines on the same graph paper and find out where they cross, but another way is by using a method called substitution. Here is how it might go.
2x=3y+4
x-5y=6 Take equation number 2 and change it like this. x = 5y + 6. See what I did there?. Now substitute 5y + 6 into the first equation for x. Like this

2(5y + 6) = 3y + 4 Multiply out the bracket

10y + 12 = 3y + 4 Now bring the 3y to the left and change it's sign to neg, and bring the +12 to the right and change it's sign to a neg.

10y - 3y = 4 - 12 Add the y's and the numbers

7y = -8

y = -8/7 So your answer is not 1

Now substitute y into the second equation to get x

x = 5y + 6
x = 5(-8/7) + 6
x = -40/7 + 6
x = -40/7 + 42/7
x = 2/7 So the answer is not -2

The point of intersection is (2/7, -8/7)

or (0.2857, -1.143)

The intesection of the two lines is where their respective equations in slope-intercept form equal each other:

2x = 3y + 4
3y = 2x - 4
y = 2/3 x - 4/3

x - 5y = 6
- 5y = - x + 6
y = 1/5 x - 6/5

y = y, so

2/3 x - 4/3 = 1/5 x - 6/5
15(2/3 x) - 15(4/3) = 15(1/5 x) - 15(6/5)
10x - 20 = 3x - 18
10x - 3x = 20 - 18
7x = 2
x = 2/7

and

y = 2/3(2/7) - 4/3
y = 4/21 - 4/3
y = 4/21 - 28/21
y = - 24/21
y = - 8/7

Point of Intersection (2/7, - 8/7)
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First of all, your answer is incorrect. You can double check by plugging in your x and y values into any one of the equation and if it is right, the numbers on both sides of the equal sign will be the same. For this, it is not.