Match Sticks Mystery

while the other solution is correct, i will show u how to think this through

if you add any 2 or 1 matches to four, it can become only 9 . so we look at the cases and see that moving 1 stick in the LHS will never make it big enough for nine and hence, the leading digit remains a 4. $$ now look at 5 in the LHS. does it have capability to lose a match. no! we move on to 7. it can lose its top to become a one , but then the maximum possible product would be $85\times 13=1105$ . this doe not have 4 as leading digit, so we move onto 3. but in the same case as 5, it cant lose 1 stick. we conclude that the 6 must lose a stick. $$ the only way(s) the 6 would make sense are . at the latter case $95*73$ which will not have 4 as leading digit. we go to the scenario where 6 only loses a stick. the possible gains are to 5. but if five gained, the 2 possibles would be $59\times 73=4307,56\times 73=4088$ . since non of this could be created by altering two sticks, we conclude 7 or 3 has to gain. you cannot add one stick to 7 and make sense of it. we give it to three who can only become9 and 6. we check and see the case with six doesnot make sense. we resort to nine and:

When we move the match stick from 6 to 3, forming 5 and 9, on the left and add 2 sticks on 7 to make 3 on the right. The new equation will be: $55\times 79$ = 4345 as shown above.

only noticeable options i saw on the left side to move a stick was turn the 6 into a 5 or the 7 into a 1, and turning the 7 to a 1 makes it impossible for the number to even reach 4 digits let alone still be true. then i just made the 3 into a 9 and it worked out rather easily. Only took a minute or so with not much trial and error involved!