What does “two-by-six crashing" mean?

As the other answers have noted, "a two-by-six" should be interpreted the same way as "a two-by-four", just a slightly larger version; it refers to a particular size of cut lumber.

Your confusion seems to come from mis-parsing the grammar of the sentence. You may be misinterpreting "crashing" as a noun that is being modified by "two-by-six", analogously to the sentence "I would send a large envelope through the mail."

However, in this sentence, "crashing" is a participle modifying "two-by-six", describing the manner in which it would go through the canvas (violently). It should be parsed analogously to the sentences "I will send a ball flying through the air" or "He sent the child laughing from the room." On its own, "two-by-six crashing" is not a phrase with any particular meaning.

An alternate way to phrase the sentence might be, "the last thing they needed now was to cause a two-by-six board to crash through a Vasari canvas."

A two-by-six is a board that’s just like a two-by-four — except that it’s wider. :)

There are other measures of lumber like this, such as a four-by-four. All of them are industry-specific terms that do not measure out to the exact size their nominal dimensions might otherwise lead you to wrongly infer.

This is because they were originally the dimensions used for green, unfinished lumber, and the subsequent finishing necessarily trimmed a bit from them. Nonetheless, the exact dimensions listed above are the actual ones that people require and expect. It’s just too awkward to adjust the language to funny fractions.

Hitting something with a 2x6 piece of lumber does more damage than hitting something with a 2x4 piece of lumber-- although maybe not exactly 1.5 times as much.

Hit me with a two by four

is a fairly common expression. According to our own @RegDwigHt in his answer to the ELU question What does "hit me like a two-by-four" mean?

it means

..... that the observation was a big surprise or a great shock; an aha experience or a eureka moment; an eye-opener.

@BorroO says

"It hit me like a two-by-four" means that you've been hit pretty hard

@mickyf says:

This may have derived from the story about how to handle Mules. "First" (clobbering mule with 2x4), "you have to get their attention."

All these answers were given before references were mandatory. Being hit by a two by four is such a common expression that I am not going to give a reference, but I will give a reference for getting the mule's attention. See Psychology Today, Changing the Mind of the Mule Why don't two-by-fours work as a management tool?

Dan Brown was referring to a Vasari canvas print, a piece of wall art, upon which a well-wielded two by six would inflict a great deal of damage.

We call them "six-by-two" in New Zealand. It's a piece of wood that's common here.