Calculating Jump Height with Higher Gravity: Formula and Tips | Help Needed

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I am trying to find out how far something can jump off the ground with a gravity that is greater than earth. If I have an inital velocity of the jump and the specified gravity that is pushing against the object, what formula would I use to find out how high the object can jump?

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I hope you mean that the "specified gravity" is pulling on the object! Gravity does not "push".

You use the same formula as you would on earth. If the gravitational acceleration is g, then the formula for height is y= (-g/2)t^2+ vt where v is the initial velocity of the jump. You can find the maximum value of y, perhaps by completing the square, to be v2/2g.

If, by "a gravity that is greater than earth", you already know the acceleration due to gravity on this other planet, just use that for g. If, instead, you only know the mass and radius of the planet, you have a little more work to do.

If the planet has mass M and radius R, the acceleration due to gravity, at the surface of the planet is g= GM/R2 where G is the "universal gravitational constant".
 
So if I have a kangaroo on planet Y with a specified gravity of 12m/s^2. If he jumps with an inital velocity of 8m/s, how far would he travel?