-Literally translated, "there are so many journalists outside" would be "ci sono cosí tanti giornalisti fuori" in italian, 'cosí' (a sort of reinforcement) would have to be added, but the sentence in this exercise is without 'cosí'.... -"molti" and "tanti" are actually interchangeable in italian, so your alternative is indeed correct!
(In my humble opinion)'Tanto' and 'molto' both have the identical function and are usually interchangeable: they add the meaning of 'large quantity' both in numbers or extension...they both have superlative forms (tanto:tantissimo/molto:moltissimo), and change their desinences for gender/number (tanto/tanta/tanti/tante;molto/molta/molti/molte); so, as adjectives, there really is no difference nor it is incorrect to use "tanti" or "molti giornalisti". The only difference I can think of is when they are added as adverbs to adjectives...'molto' brings the adj. to superlativ form (-issimo), while 'tanto' can also create a subordinate clause of cause-effect: eg. sono molto felice (I am really/very happy), sono tanto felice da non accorgermi che fa freddo e sta piovendo (I am so happy not to realize that it's cold and it's raining). (pls forgive my english if there are mistakes).
Molto refers to things you cannot count e.g molto aqua. I think tanto refers to things like e.g. eggs, people , books. Does that help? I expect there are exceptions , but it's a starting point for you. In English we refer to many journalists, but much water. We can count the journalists, but we would have to measure the water
My sense of tante molte is that, when they both mean "many", tante is more "many" than molte. Two examples I thought of:
There were many people (tante persone) in the room and no seats could be found.
There were many people (molte persone) in the room and it was difficult to find a seat.