Thanks for clearing that up.
Let's look at this in pieces.
1) Lim as x--> infinity of 2x = infinity
2) Lim as x--> infinity of sin(x) will approach -1, 0, or 1.
Think of the unit circle. The smallest sin(x) can be is -1 and the largest sin(x) can be is +1.
But this really doesn't matter as -1 or +1 will not have an effect when added to infinity.
Infinity + anything = infinity
So the limit is infinity.