**Would someone be able to go over how I would solve this problem. Thank you.**

Did they not cover this stuff in class and in your textbook? Ouch! For which parts are you needing lessons? Do you understand derivatives at all? Etc.

The tangent to the curve x^{3}+3x^{2}-1 at x=0 and intersects the curve at another point.

This is not actually a complete sentence, and the "curve" equation isn't even an equation! Did they maybe actually say "y = x^3 + 3x^2 - 1", or "f(x)="?

Determine the co-ordinates of the other point and find the equation of the tangent at the second point. Graph the function and the tangents.

The question mentions "the tangent", being one; the instructions mention "the tangents", being two or more. So clearly something is missing here.

Please reply with the full and exact text of the exercise, the complete instructions, and a clear listing of your thoughts and efforts so far. Thank you!