X-intercepts are the point or points, if any, where a graph crosses the x-axis. If one thinks about the coordinates of the points on the x-axis you will find that while the x-coordinates can be any number, the y-coordinates of all the points on the x-axis are zero. So to find an x-intercept, substitute zero for the y, NOT THE X, in the equation. Your equation, y=x^2+6, becomes:
(0) = x^2 + 6
Solving for x:
Subtract 6
0 - 6 = x^2 + 6 -6
-6 = x^2
Since it is impossible to square a Real number and get a negative number like -6, this equation has no solution. This means that there are NO x-intercepts for your equation, y=x^2+6.
Y-intercepts are where a graph crosses the y-axis. Using reasoning similar to that used for x-intercepts we find that all points on the y-axis have an x-coordinate which is zero. So to find a y-intercept, substitute a zero for the x, NOT THE Y, in the equation. Your equation, y = x^2 + 6, becomes:
y = (0)^2 + 6
y = 0 + 6
y = 6
So the only y-intercept is (0,6).