Fourier transform of the product I'm new at signal processing. I also don't know if this is the right section to post. I have this problem: I must calculate the Fourier transform of the signal shown in the image below 



I have expressed this as $$\require{cancel}\cancel{\Delta\left(\frac{t-4}{4}\right)\textrm{rect}\left(\frac{t-2}{4}\right)}$$

I read that the Fourier transform of a time-domain product equals the convolution of the two transforms in frequency domain but I don't know how to proceed, can you kindly help me?
First of all, your graph does not match the equation you gave for the function. From the hint of msm, we should use the following property of the Fourier Transform:

$$
\mathcal{F}\left\{\frac{d}{dt}x(t)\right\}=j2\pi fX(f)
$$

with 

$$
\mathcal{F}\{x(t)\} = X(f)
$$

Now, what's the derivative of your function in the graph? Its given by

$$
x'(t)=\frac{1}{4}\text{rect}\left(\frac{t-2}{4}\right) - \text{rect}(t-\frac{9}{2})
$$

Now, let's do the Fourier Transform of the derivative:

$$
j2\pi fX(f)=\text{sinc}(4f)\exp(-j2\pi 2f) - \text{sinc}(f)\exp(-j2\pi \frac{9}{2}f)
$$

with $\text{sinc}(x)=\frac{\sin(\pi x)}{\pi x}$.

Now, finally dividing by $j2\pi f$ you get

$$
X(f) = \frac{1}{j2\pi f}\left(\text{sinc}(4f)\exp(-j2\pi2f)-\text{sinc}(f)\exp(-j2\pi\frac{9}{2}f)\right).
$$

You can try to simplify this expression, but it might not yield something that is better to understand.