This is not exactly step-by-step, but it will give you an outline of what's needed, and hopefully you can fill in the details.

Step 1. Collect the x terms together, and also the y terms, and complete the square in both x and y. That should lead to the result .

Step 2. Divide by 4, so as to get 1 on the right-hand side: . You should recognise that as the equation of an ellipse with its centre at (–1,4) and semi-axes √2 and 2 (the square roots of the denominators).

Step 3. You can then write down the parametric equations in the form , .