What solution does Benvolio suggest to Romeo in Act 3, Scene 1?
Benvolio tells Romeo to follow his lead. Look at other ladies. There are other people than this Rosalind girl. Benvolio hopes that if Romeo sees that there are other girls that may return his affections that will forget Rosalind.
This is also an example of dramatic irony. Romeo has no clue what will happen when takes Benvolio's advice but we as the audience knows that he will meet Juliet soon.
In the beginning of the play, Romeo is lovesick over Rosaline. Romeo ends up reading the Capulet guest list for the party and Romeo's friends including Mercutio and Benvolio decide to go. Benvolio encourages Romeo to look at other girls at the party and to forget Rosaline.
The solution Benvolio suggest to Romeo is to go away from Verona before the guards come and attack him.
Before in the story, the prince had already talked to Montague and Capulet three times so both Romeo and Benvolio were aware of the consequences that they were going to receive.
He told him not to go depressed just because of one woman, that would be other "fishes" for him to catche. Don't get sad just over one person and move on to the future. Your future would be ruined if you keep on brooding on the past. If you look at the other girls, you may soon forget about Rosalind and explore better opportunires. This was good advice as he later on meet another love live but a tragic one just the same with Juliet soon. He must free himself of the misery that he is creating himself and cure his lovesickness that prevents him from pursuing other options
to leave the city
benvolio suggests romeo to go away before he is caught otherwise he'll be exiled by the Prince
In order for Romeo to recover from his deep melancholy arousing from his unrecoited love for Rosaline, Benvolio suggests that he free himself of his sadness by "giving liberty unto thine eyes" and "examine other beauties." (Act 1, Scene 1) In other words, Benvolio is suggesting that if Romeo just starts looking around at other beautiful girls he can cure his lovesickness.
If you're talking about Act I, he pretty much tells Romeo that there's more fish in the sea. Don't go all emo just because the one you want is sworn to chasity.
OK wait, if you mean Act I Scene 1, that's when Romeo confesses his love, and Benvolio says:
Listen to me, forget about her.
In Act III, Scene 1, after the death of Mercutio, Benvolio says:
Romeo, away, be gone!
The citizens are up, and Tybalt slain.--
Stand not amaz'd. The prince will doom thee death
If thou art taken. Hence, be gone, away!
He then asks:
Why dost thou stay?
I'm not sure if this is what you're looking for, but it came to mind.