A#44: This question is a classic pot-odds/EV question, and really boils down to your equity in the hand, which in turn boils down to the range you put your opponent on. In other words: REDi.
Reads: A LAG in a six-max game is opening pretty wide UTG. Something like any pair and any two broadway cards. When he flats your MP 3bet, however, we can eliminate some of this range. For example, he's probably 4betting QQ-AA, AKs, AKo, and maybe even AQs. If we take these out his initial range, we're left with JJ-22,AJs-ATs,KTs+,QTs+,JTs,AQo-ATo,KTo+,QTo+,JTo
Now, the question is, can we narrow it any further given his check-raise on the 3h-4h-8c flop? Well, this strongly depends on his individual traits and tendencies. Is he trappy? What kinds of hands is he putting us on? And so on. Unfortunately, we're not given any of this information, so we have to assume he's an ABC LAg. Said another way, he's X/R'ing us with some kind of equity, and doesn't have complete air. Let's narrow our read by keeping all the previous pairs (TT-22), and suited overcards from the previous range. Call it: JJ-22,QhJh,QhTh,JhTh (Note that any of the previous range that included an A or a K is removed because we hold those heart blockers in our own hand.)
Estimate: Against this range on this flop, our equity is almost exactly 50%. The pot is $1320, and it's $685 to you to call. Our EV here is: [(50%)($1320) - (50%)($685)] = +$317.50.
Decide: This is a significantly plus EV call, therefore we're on a Value line.
The main thing to take away here is that it's all about your read on the other player. Once you've placed your opponent on a preflop range, you then work to narrow that range based on logically dissecting his actions relative to yours and the board texture. Once you've done that, the rest is actually fairly easy to make the correct decision.
All-in for now...