First,
welcome to subsim...you came to the right place for help! First off, if this is your first time playing a submarine sim, it's quite an adjustment from other games/sims. If you're having trouble with destroyers, my first guess is that they may have spotted your sub or it's scope. Stealth is the name of the game with subs. I would recommend reading some of the sticky threads for excellent tips and advice. SH4 is an excellent game, so try not to get discouraged. Once you get a hang of things, there are some wonderful mods that can be found here in the mods section. Anyways, best of luck, and hang in there!
Good hunting,
Howler