Let's assign some variables...
Let $r$ = the number of roses in the garden
Let t = the number of tulips in the garden
Since garden has only equal number of roses and tulips, we know that $r = t$

QUANTITY A: Twice the probability that both the flowers selected are roses
P(both flowers are roses) = P(1st flower is a rose AND 2nd flower is a rose)
= P(1st flower is a rose) x P(2nd flower is a rose)

= $\frac{r}{r+t}$ x $\frac{r-1}{r+t-1}$

= $\frac{r(r-1)}{(r+t)(r+t-1)}$

We want TWICE that probability, which means QUANTITY A = $\frac{2r(r-1)}{(r+t)(r+t-1)}$


QUANTITY B: Probability that one of the flowers selected is rose and the other is tulip
P(select one rose and one tulip) = P(1st flower is a rose AND 2nd flower is a tulip OR 1st flower is a tulip AND 2nd flower is a rose)
= [P(1st flower is a rose) x P(2nd flower is a tulip)] + [P(1st flower is a tulip) x P(2nd flower is a rose)]

= [$\frac{r}{r+t}$ x$\frac{t}{r+t-1}$] + [$\frac{t}{r+t}$ x $\frac{r}{r+t-1}$]

= $\frac{rt}{(r+t)(r+t-1)}$ + $\frac{tr}{(r+t)(r+t-1)}$

= $\frac{2rt}{(r+t)(r+t-1)}$

So we have the following:
QUANTITY A: $\frac{2r(r-1)}{(r+t)(r+t-1)}$

QUANTITY B: $\frac{2rt}{(r+t)(r+t-1)}$

Multiply both quantities by $(r+t)(r+t-1)$ to get:
QUANTITY A: $2r(r-1)$
QUANTITY B: $2rt$

Divided both quantities by $2r$ to get:
QUANTITY A: $r-1$
QUANTITY B: $t$

Since $r = t$, we can rewrite Quantity B as follows:
QUANTITY A: $r-1$
QUANTITY B: $r$

At this point we can clearly see that Quantity B is greater

Answer: B