Was it possible for Jesus to sin?
It depends on how you define "possible."
If "possible" means, "Did he have the brain and the natural capacities to discern a temptation and choose it," then yes. He had a brain and he had a will. If he didn't, he would not have been a human being.
He's discerning, he's thinking, he's feeling. He knows what hunger is. He knows what sexual arousal is, and so on. He knows these things! He's a human being. If he didn't have those then he wouldn't be a human being.
But historically, the word "possible" has another meaning, a very important meaning—namely, a moral ability. There's a natural ability, which he must have in order to be accountable and human, and a moral ability, which he did not have.
A moral ability is when you are bad enough to choose sin. There's enough badness in you that you can choose sin. Jesus didn't have it. There was no badness in Jesus.
Therefore he did not ever, in his willing and feeling and in his perception of temptation, he didn't ever rise to the point of going there. Because that's evil in us!
Evil is not just acting. Evil is wanting to act in a certain way. Craving money is as bad as having money that you stole. "I want the praise of man, I want that money, I want that lustful object"—and those wants are evil.
Jesus never had any of those. He was perfect. And if you don't have those, you can't do it!
You can't choose to sin if there is no desire to sin. And Jesus never had any desire to sin. Therefore he couldn't sin.
And so, in those two ways, it was possible and it wasn't possible for Jesus to sin.