Determining optimal consumption bundle
I will only provide a general outline here since this is clearly a homework question. 



You know that you should have, at an optimal point, that the marginal utility of each of your two goods is equal and so you can use: 

$$MU_x=MU_y$$

You also have a budget constraint, yes? something like: 

$$x+y=P_x(initial endowment of x) + P_y(initial endowment of y) + Income$$



Now you have enough equations to solve, I think. Isolate either x or y using your budget constraint. To be concrete here, I will assume you isolate x. 

Take this representation of x and plug it in for x where you've equated your marginal utilities. This should allow you to solve for y in terms of exogenous factors. Take this representation of y and plug it back into $MU_x$. This gives both x and y in terms of exogenous factors. 

So, all you are doing is equating marginal utilities and also using the budget constraint to express the optimal bundle (optimal amounts of goods x,y) in terms of exogenous factors.