This is the scene with the cap and gown in Act IV, Scene III. The scene is a bit complicated, so here's a quote from a little earlier in the play, where Petruchio is planning how he will tame the shrew. (Act IV, Scene I)

My falcon now is sharp and passing empty;

And till she stoop she must not be full-gorged,

For then she never looks upon her lure.

Another way I have to man my haggard,

To make her come and know her keeper's call,

That is, to watch her, as we watch these kites

That bate and beat and will not be obedient.

She eat no meat to-day, nor none shall eat;

Last night she slept not, nor to-night she shall not;

As with the meat, some undeserved fault

I'll find about the making of the bed;

And here I'll fling the pillow, there the bolster,

This way the coverlet, another way the sheets:

Ay, and amid this hurly I intend

That all is done in reverend care of her;

And in conclusion she shall watch all night:

And if she chance to nod I'll rail and brawl

And with the clamour keep her still awake.

This is a way to kill a wife with kindness;

And thus I'll curb her mad and headstrong humour.

He that knows better how to tame a shrew,

Now let him speak: 'tis charity to show.

This image shows events from a bit later: Petruchio has just rejected a cap he had ordered for Kate (seen on the ground) over her wishes, because it was not good enough for her, and is now analysing and finding fault with a gown he had ordered for her. It too will soon be rejected, despite Kate's liking for it, until she learns to obey her husband's will. By the end of it, he'll literally have her agreeing the sun is the moon, if he says so.

A slightly different version by Charles Rolls

Catherine and Petruchio (from William Shakespeare's 'The Taming of the Shrew', Act iv, Sc.iii) - the original by C. R. Leslie. Exhibited at the Royal Academy in 1832 The caption for the original painting (owned by the National Trust at Petworth) was:

Petruchio: Brav'd in mine own house with a skein of thread! Away! thou rag, thou quantity, thou remnant: Or I shall so be-mete thee with thy yard, As thou shalt think on prating whilst thou livs't! I tell thee, I, that thou hast marr'd her gown.

Taylor: Your worship is deceiv'd, the gown is made Just as my master has direction Grumio gave order how it should be made.

Grumio: I gave no order, I gave the stuff."

Experts have asserted to the National Trust that the tailor, second from right, was posed for by David Wilkie, the artist - aged 47 in 1832.